Free exponents worksheets - Free Printable

Exponents Worksheet Solution

The worksheet involves solving problems related to exponents. Here is the step-by-step solution for each problem:

---

#### 1 a. \( 4^4 \)
- \( 4^4 \) means \( 4 \times 4 \times 4 \times 4 \).
- Calculate step-by-step:
\[
4 \times 4 = 16
\]
\[
16 \times 4 = 64
\]
\[
64 \times 4 = 256
\]
- Answer: \( 256 \)

#### 1 b. \( 19^2 \)
- \( 19^2 \) means \( 19 \times 19 \).
- Calculate:
\[
19 \times 19 = 361
\]
- Answer: \( 361 \)

#### 2 a. \( 2^{10} \)
- \( 2^{10} \) means \( 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \).
- This can be calculated as:
\[
2^2 = 4, \quad 2^4 = 16, \quad 2^8 = 256, \quad 2^{10} = 256 \times 4 = 1024
\]
- Answer: \( 1024 \)

#### 2 b. \( 47^2 \)
- \( 47^2 \) means \( 47 \times 47 \).
- Calculate:
\[
47 \times 47 = 2209
\]
- Answer: \( 2209 \)

#### 3 a. \( 2^1 \)
- Any number raised to the power of 1 is the number itself.
- Answer: \( 2 \)

#### 3 b. \( 8^1 \)
- Any number raised to the power of 1 is the number itself.
- Answer: \( 8 \)

#### 4 a. \( 0^{23} \)
- Any non-zero number raised to any power is 0 (except \( 0^0 \), which is undefined).
- Answer: \( 0 \)

#### 4 b. \( 1000^3 \)
- \( 1000^3 \) means \( 1000 \times 1000 \times 1000 \).
- Calculate:
\[
1000 \times 1000 = 1,000,000
\]
\[
1,000,000 \times 1000 = 1,000,000,000
\]
- Answer: \( 1,000,000,000 \)

#### 5 a. \( 1^6 \)
- Any number raised to any power is 1 if the base is 1.
- Answer: \( 1 \)

#### 5 b. \( 1^{26} \)
- Any number raised to any power is 1 if the base is 1.
- Answer: \( 1 \)

#### 6 a. \( 7^2 \)
- \( 7^2 \) means \( 7 \times 7 \).
- Calculate:
\[
7 \times 7 = 49
\]
- Answer: \( 49 \)

#### 6 b. \( 3^3 \)
- \( 3^3 \) means \( 3 \times 3 \times 3 \).
- Calculate:
\[
3 \times 3 = 9
\]
\[
9 \times 3 = 27
\]
- Answer: \( 27 \)

#### 7 a. \( 87^2 \)
- \( 87^2 \) means \( 87 \times 87 \).
- Calculate:
\[
87 \times 87 = 7569
\]
- Answer: \( 7569 \)

#### 7 b. \( 2^7 \)
- \( 2^7 \) means \( 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \).
- This can be calculated as:
\[
2^2 = 4, \quad 2^4 = 16, \quad 2^7 = 16 \times 8 = 128
\]
- Answer: \( 128 \)

#### 8 a. \( 63^2 \)
- \( 63^2 \) means \( 63 \times 63 \).
- Calculate:
\[
63 \times 63 = 3969
\]
- Answer: \( 3969 \)

#### 8 b. \( 8^2 \)
- \( 8^2 \) means \( 8 \times 8 \).
- Calculate:
\[
8 \times 8 = 64
\]
- Answer: \( 64 \)

#### 9 a. \( 0^{73} \)
- Any non-zero number raised to any power is 0 (except \( 0^0 \), which is undefined).
- Answer: \( 0 \)

#### 9 b. \( 37^2 \)
- \( 37^2 \) means \( 37 \times 37 \).
- Calculate:
\[
37 \times 37 = 1369
\]
- Answer: \( 1369 \)

#### 10 a. \( 5^4 \)
- \( 5^4 \) means \( 5 \times 5 \times 5 \times 5 \).
- Calculate step-by-step:
\[
5 \times 5 = 25
\]
\[
25 \times 5 = 125
\]
\[
125 \times 5 = 625
\]
- Answer: \( 625 \)

#### 10 b. \( 31^1 \)
- Any number raised to the power of 1 is the number itself.
- Answer: \( 31 \)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1 \text{ a. } 256 & 1 \text{ b. } 361 \\
2 \text{ a. } 1024 & 2 \text{ b. } 2209 \\
3 \text{ a. } 2 & 3 \text{ b. } 8 \\
4 \text{ a. } 0 & 4 \text{ b. } 1,000,000,000 \\
5 \text{ a. } 1 & 5 \text{ b. } 1 \\
6 \text{ a. } 49 & 6 \text{ b. } 27 \\
7 \text{ a. } 7569 & 7 \text{ b. } 128 \\
8 \text{ a. } 3969 & 8 \text{ b. } 64 \\
9 \text{ a. } 0 & 9 \text{ b. } 1369 \\
10 \text{ a. } 625 & 10 \text{ b. } 31 \\
\end{array}
}
\]