Class 7 Exponents and Powers worksheet with multiple-choice questions on exponent rules and calculations.
A math worksheet titled "Exponents and Powers" for Class 7, featuring questions on exponent rules, including finding values, simplifying expressions, and solving equations with exponents.
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Step-by-step solution for: Grade 7 - Exponents and Powers | Math Practice, Questions, Tests ...
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Show Answer Key & Explanations
Step-by-step solution for: Grade 7 - Exponents and Powers | Math Practice, Questions, Tests ...
Here is the complete solution to all the problems in the worksheet, explained step-by-step.
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A) 8⁴
This means multiplying 8 by itself 4 times:
8 × 8 × 8 × 8 = 64 × 64 = 4096
B) (-8)³
This means multiplying -8 by itself 3 times:
(-8) × (-8) × (-8) = 64 × (-8) = -512
*(Note: Odd power of a negative number is negative.)*
C) 9⁴
9 × 9 × 9 × 9 = 81 × 81 = 6561
D) (-7)³
(-7) × (-7) × (-7) = 49 × (-7) = -343
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\(\left(-\frac{2}{2}\right)^2 \times \left(\frac{1}{2}\right)^3 \times \left(\frac{2}{3}\right)^3 = ?\)
First, simplify each term:
- \(\left(-\frac{2}{2}\right)^2 = (-1)^2 = 1\)
- \(\left(\frac{1}{2}\right)^3 = \frac{1}{8}\)
- \(\left(\frac{2}{3}\right)^3 = \frac{8}{27}\)
Now multiply them:
\(1 \times \frac{1}{8} \times \frac{8}{27} = \frac{1 \times 1 \times 8}{1 \times 8 \times 27} = \frac{8}{216} = \frac{1}{27}\)
✔ Answer: \(\frac{1}{27}\)
---
We are given expressions and need to choose the correct simplified form.
Let’s evaluate each option:
A) \(5^2 \times 5^4 \times 5^4 \times 5^7\)
When multiplying same bases, add exponents:
\(5^{2+4+4+7} = 5^{17}\)
B) \(2^5 \times 2^5 = 2^{10}\)
C) \(3^6 \times 3^7 \times 3^5 = 3^{6+7+5} = 3^{18}\)
D) \(3^9 \times 3^4 \times 3^3 + 3^8 = 3^{16} + 3^8\) — This cannot be simplified further into a single exponent.
The question says “simplify and write in exponential form”, implying a single term. All options A, B, C are already simplified into single exponents. But since it’s multiple choice with one correct answer expected, and all A, B, C are valid simplifications, we must check if there's a typo or context.
However, looking at the structure, Option A has 4 terms multiplied — perhaps it's meant to test combining multiple exponents. But since all are correct as written, and no instruction says "choose only one", but typically such questions expect one best answer — A is the most complex and likely the intended answer.
But wait — let’s re-read: “Simplify the following and write the answer in exponential form” — and lists 4 options. It seems like it’s asking which expression simplifies to what? Actually, it’s ambiguous.
Looking again, it’s probably asking: *Which of these expressions is correctly simplified?* But they are already written in exponential form.
Actually, I think this is a multiple-choice question where you pick the correct simplification — but since all are correct, perhaps the question is misphrased.
Alternatively, maybe it’s asking: “Simplify each and see which matches an option?” But no original expression is given.
Wait — rereading carefully: It says “Simplify the following” — but then lists 4 choices labeled A, B, C, D — so likely, each letter is a separate expression to simplify, and we are to pick the correct simplified form? But that doesn’t make sense.
Actually, looking at the format, this is likely a single question with 4 options, and we are to pick which one is correct after simplifying... but without an original expression.
This seems like a formatting error. But in standard worksheets, this usually means: Simplify each of these expressions and match to the correct simplified form — but here, they are already simplified.
Perhaps the intention is to recognize that all are correct, but since it’s “choose correct answer(s)”, and later questions say “choose correct answer(s)”, this might be a trick.
But to proceed logically, since all A, B, C are correct simplifications, and D is not a single exponent, perhaps the question expects A, B, C as correct.
But since it’s listed under “Answer the questions” and not “Choose correct answer(s)”, and no instruction to select multiple, I’ll assume it’s a single-answer question, and A is the most comprehensive example.
However, upon closer inspection, I believe this may be a misprint, and perhaps it was meant to ask for simplification of a single expression. Since we can’t resolve ambiguity, I'll note that A, B, C are all correctly simplified.
But to match typical worksheet design, let’s assume the question is: Which of these equals \(5^{17}\)? → Then A.
I think safest is to say:
✔ All A, B, C are correct simplifications. D is not a single exponent.
But since the worksheet likely expects one answer, and A has the most terms, I’ll go with A.
Actually, let me check online or standard practice — no, better to be accurate.
Given the ambiguity, I’ll provide the simplified forms:
- A → \(5^{17}\)
- B → \(2^{10}\)
- C → \(3^{18}\)
- D → \(3^{16} + 3^8\) (not a single exponent)
So if the question is “which is in exponential form”, then A, B, C are, D is not.
But since it’s “simplify and write in exponential form”, and they are already written, perhaps it’s testing recognition.
I think for the purpose of this, I’ll say:
✔ Correct answers: A, B, C
But since the format might expect one, and later questions have single letters, perhaps it’s a mistake.
To move forward, I’ll note that A is correct as per common interpretation.
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Substitute x=1, y=5:
\(\left(\frac{1}{5}\right)^1 = \frac{1}{5}\)
✔ Answer: \(\frac{1}{5}\)
---
A) \(5 \times 10^2 + 0 \times 10^3 + 0 \times 10^3 + 5 \times 10^5 + 9 \times 10^6\)
Wait — there’s a typo: two \(0 \times 10^3\). Probably should be different powers.
Assuming it’s:
\(5 \times 10^2 + 0 \times 10^3 + 0 \times 10^4 + 5 \times 10^5 + 9 \times 10^6\)
Calculate each:
- \(9 \times 10^6 = 9,000,000\)
- \(5 \times 10^5 = 500,000\)
- \(0 \times 10^4 = 0\)
- \(0 \times 10^3 = 0\)
- \(5 \times 10^2 = 500\)
Add: 9,000,000 + 500,000 = 9,500,000 + 500 = 9,500,500
B) \(0 \times 10^1 + 9 \times 10^4 + 2 \times 10^2 + 1 \times 10^5 + 0 \times 10^7\)
Calculate:
- \(1 \times 10^5 = 100,000\)
- \(9 \times 10^4 = 90,000\)
- \(2 \times 10^2 = 200\)
- Others are 0
Add: 100,000 + 90,000 = 190,000 + 200 = 190,200
✔ So the numbers are:
- A → 9,500,500
- B → 190,200
---
\(\left(\frac{-5}{3}\right)^3 \times \left(\frac{1}{3}\right)^2 = ?\)
Compute each part:
- \(\left(\frac{-5}{3}\right)^3 = \frac{(-5)^3}{3^3} = \frac{-125}{27}\)
- \(\left(\frac{1}{3}\right)^2 = \frac{1}{9}\)
Multiply:
\(\frac{-125}{27} \times \frac{1}{9} = \frac{-125}{243}\)
✔ Answer: \(\frac{-125}{243}\)
---
Factor out \(2^p\):
\(2^p + 2^{p+1} = 2^p + 2^p \cdot 2^1 = 2^p (1 + 2) = 2^p \cdot 3\)
Set equal to 24:
\(3 \cdot 2^p = 24\)
Divide both sides by 3:
\(2^p = 8\)
Since \(8 = 2^3\), so:
\(p = 3\)
✔ Answer: 3
---
\(\left(\frac{4}{2}\right)^4 \div \left(\frac{1}{2}\right)^3 = ?\)
First, simplify:
\(\left(\frac{4}{2}\right)^4 = 2^4 = 16\)
\(\left(\frac{1}{2}\right)^3 = \frac{1}{8}\)
Now divide:
\(16 \div \frac{1}{8} = 16 \times 8 = 128\)
Look at options:
a. 4096/8 = 512
b. 128/1 = 128 ✔
c. 256/8 = 32
d. 1024/32 = 32
✔ Answer: b. 128
---
Start: 1 jasmine
After 1 week: 2
After 2 weeks: 4 = 2²
After 3 weeks: 8 = 2³
...
After x weeks: \(2^x\)
✔ Answer: a. \(2^x\)
---
## ✔ Final Answers Summary:
(1)
A) 4096
B) -512
C) 6561
D) -343
(2) \(\frac{1}{27}\)
(3) A, B, C are correct simplifications (D is not a single exponent) — but if forced to choose one, A is most comprehensive.
(4) \(\frac{1}{5}\)
(5)
A) 9,500,500
B) 190,200
(6) \(\frac{-125}{243}\)
(7) \(p = 3\)
(8) b. 128
(9) a. \(2^x\)
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Let me know if you want any part explained further!
---
(1) Find value of following
A) 8⁴
This means multiplying 8 by itself 4 times:
8 × 8 × 8 × 8 = 64 × 64 = 4096
B) (-8)³
This means multiplying -8 by itself 3 times:
(-8) × (-8) × (-8) = 64 × (-8) = -512
*(Note: Odd power of a negative number is negative.)*
C) 9⁴
9 × 9 × 9 × 9 = 81 × 81 = 6561
D) (-7)³
(-7) × (-7) × (-7) = 49 × (-7) = -343
---
(2)
\(\left(-\frac{2}{2}\right)^2 \times \left(\frac{1}{2}\right)^3 \times \left(\frac{2}{3}\right)^3 = ?\)
First, simplify each term:
- \(\left(-\frac{2}{2}\right)^2 = (-1)^2 = 1\)
- \(\left(\frac{1}{2}\right)^3 = \frac{1}{8}\)
- \(\left(\frac{2}{3}\right)^3 = \frac{8}{27}\)
Now multiply them:
\(1 \times \frac{1}{8} \times \frac{8}{27} = \frac{1 \times 1 \times 8}{1 \times 8 \times 27} = \frac{8}{216} = \frac{1}{27}\)
✔ Answer: \(\frac{1}{27}\)
---
(3) Simplify and write the answer in exponential form
We are given expressions and need to choose the correct simplified form.
Let’s evaluate each option:
A) \(5^2 \times 5^4 \times 5^4 \times 5^7\)
When multiplying same bases, add exponents:
\(5^{2+4+4+7} = 5^{17}\)
B) \(2^5 \times 2^5 = 2^{10}\)
C) \(3^6 \times 3^7 \times 3^5 = 3^{6+7+5} = 3^{18}\)
D) \(3^9 \times 3^4 \times 3^3 + 3^8 = 3^{16} + 3^8\) — This cannot be simplified further into a single exponent.
The question says “simplify and write in exponential form”, implying a single term. All options A, B, C are already simplified into single exponents. But since it’s multiple choice with one correct answer expected, and all A, B, C are valid simplifications, we must check if there's a typo or context.
However, looking at the structure, Option A has 4 terms multiplied — perhaps it's meant to test combining multiple exponents. But since all are correct as written, and no instruction says "choose only one", but typically such questions expect one best answer — A is the most complex and likely the intended answer.
But wait — let’s re-read: “Simplify the following and write the answer in exponential form” — and lists 4 options. It seems like it’s asking which expression simplifies to what? Actually, it’s ambiguous.
Looking again, it’s probably asking: *Which of these expressions is correctly simplified?* But they are already written in exponential form.
Actually, I think this is a multiple-choice question where you pick the correct simplification — but since all are correct, perhaps the question is misphrased.
Alternatively, maybe it’s asking: “Simplify each and see which matches an option?” But no original expression is given.
Wait — rereading carefully: It says “Simplify the following” — but then lists 4 choices labeled A, B, C, D — so likely, each letter is a separate expression to simplify, and we are to pick the correct simplified form? But that doesn’t make sense.
Actually, looking at the format, this is likely a single question with 4 options, and we are to pick which one is correct after simplifying... but without an original expression.
This seems like a formatting error. But in standard worksheets, this usually means: Simplify each of these expressions and match to the correct simplified form — but here, they are already simplified.
Perhaps the intention is to recognize that all are correct, but since it’s “choose correct answer(s)”, and later questions say “choose correct answer(s)”, this might be a trick.
But to proceed logically, since all A, B, C are correct simplifications, and D is not a single exponent, perhaps the question expects A, B, C as correct.
But since it’s listed under “Answer the questions” and not “Choose correct answer(s)”, and no instruction to select multiple, I’ll assume it’s a single-answer question, and A is the most comprehensive example.
However, upon closer inspection, I believe this may be a misprint, and perhaps it was meant to ask for simplification of a single expression. Since we can’t resolve ambiguity, I'll note that A, B, C are all correctly simplified.
But to match typical worksheet design, let’s assume the question is: Which of these equals \(5^{17}\)? → Then A.
I think safest is to say:
✔ All A, B, C are correct simplifications. D is not a single exponent.
But since the worksheet likely expects one answer, and A has the most terms, I’ll go with A.
Actually, let me check online or standard practice — no, better to be accurate.
Given the ambiguity, I’ll provide the simplified forms:
- A → \(5^{17}\)
- B → \(2^{10}\)
- C → \(3^{18}\)
- D → \(3^{16} + 3^8\) (not a single exponent)
So if the question is “which is in exponential form”, then A, B, C are, D is not.
But since it’s “simplify and write in exponential form”, and they are already written, perhaps it’s testing recognition.
I think for the purpose of this, I’ll say:
✔ Correct answers: A, B, C
But since the format might expect one, and later questions have single letters, perhaps it’s a mistake.
To move forward, I’ll note that A is correct as per common interpretation.
---
(4) If x=1 and y=5, find the value of \(\left(\frac{x}{y}\right)^x\)
Substitute x=1, y=5:
\(\left(\frac{1}{5}\right)^1 = \frac{1}{5}\)
✔ Answer: \(\frac{1}{5}\)
---
(5) Find number for following expanded forms
A) \(5 \times 10^2 + 0 \times 10^3 + 0 \times 10^3 + 5 \times 10^5 + 9 \times 10^6\)
Wait — there’s a typo: two \(0 \times 10^3\). Probably should be different powers.
Assuming it’s:
\(5 \times 10^2 + 0 \times 10^3 + 0 \times 10^4 + 5 \times 10^5 + 9 \times 10^6\)
Calculate each:
- \(9 \times 10^6 = 9,000,000\)
- \(5 \times 10^5 = 500,000\)
- \(0 \times 10^4 = 0\)
- \(0 \times 10^3 = 0\)
- \(5 \times 10^2 = 500\)
Add: 9,000,000 + 500,000 = 9,500,000 + 500 = 9,500,500
B) \(0 \times 10^1 + 9 \times 10^4 + 2 \times 10^2 + 1 \times 10^5 + 0 \times 10^7\)
Calculate:
- \(1 \times 10^5 = 100,000\)
- \(9 \times 10^4 = 90,000\)
- \(2 \times 10^2 = 200\)
- Others are 0
Add: 100,000 + 90,000 = 190,000 + 200 = 190,200
✔ So the numbers are:
- A → 9,500,500
- B → 190,200
---
(6)
\(\left(\frac{-5}{3}\right)^3 \times \left(\frac{1}{3}\right)^2 = ?\)
Compute each part:
- \(\left(\frac{-5}{3}\right)^3 = \frac{(-5)^3}{3^3} = \frac{-125}{27}\)
- \(\left(\frac{1}{3}\right)^2 = \frac{1}{9}\)
Multiply:
\(\frac{-125}{27} \times \frac{1}{9} = \frac{-125}{243}\)
✔ Answer: \(\frac{-125}{243}\)
---
(7) If \(2^p + 2^{p+1} = 24\), find the value of p.
Factor out \(2^p\):
\(2^p + 2^{p+1} = 2^p + 2^p \cdot 2^1 = 2^p (1 + 2) = 2^p \cdot 3\)
Set equal to 24:
\(3 \cdot 2^p = 24\)
Divide both sides by 3:
\(2^p = 8\)
Since \(8 = 2^3\), so:
\(p = 3\)
✔ Answer: 3
---
(8) Choose correct answer(s)
\(\left(\frac{4}{2}\right)^4 \div \left(\frac{1}{2}\right)^3 = ?\)
First, simplify:
\(\left(\frac{4}{2}\right)^4 = 2^4 = 16\)
\(\left(\frac{1}{2}\right)^3 = \frac{1}{8}\)
Now divide:
\(16 \div \frac{1}{8} = 16 \times 8 = 128\)
Look at options:
a. 4096/8 = 512
b. 128/1 = 128 ✔
c. 256/8 = 32
d. 1024/32 = 32
✔ Answer: b. 128
---
(9) Neha plants a jasmine on her 6th birthday. Plant starts with 1 jasmine, doubles every week. How many after x weeks?
Start: 1 jasmine
After 1 week: 2
After 2 weeks: 4 = 2²
After 3 weeks: 8 = 2³
...
After x weeks: \(2^x\)
✔ Answer: a. \(2^x\)
---
## ✔ Final Answers Summary:
(1)
A) 4096
B) -512
C) 6561
D) -343
(2) \(\frac{1}{27}\)
(3) A, B, C are correct simplifications (D is not a single exponent) — but if forced to choose one, A is most comprehensive.
(4) \(\frac{1}{5}\)
(5)
A) 9,500,500
B) 190,200
(6) \(\frac{-125}{243}\)
(7) \(p = 3\)
(8) b. 128
(9) a. \(2^x\)
---
Let me know if you want any part explained further!
Parent Tip: Review the logic above to help your child master the concept of 7th grade math exponents worksheet.
