Simplifying algebraic expressions worksheet with coloring activity.

It looks like you've uploaded an image containing a math worksheet with 15 problems involving scientific notation and standard form. The task is to:

1. Solve each expression (simplify or evaluate).
2. Write the answer in standard form (i.e., regular decimal form, not scientific notation).
3. Match the answer to a color code (though the color key isn't visible here).
4. Color the corresponding section of a picture based on the answer.

Since I can't view images directly, I'll solve each problem as written, assuming they are expressions involving exponents, scientific notation, or algebraic simplification.

Let’s go through each one step by step.

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Problem 1:

8a⁰b⁷ / 16a³b

- Recall: $ a^0 = 1 $
- So numerator: $ 8 \cdot 1 \cdot b^7 = 8b^7 $
- Denominator: $ 16a^3b $
- Simplify: $ \frac{8b^7}{16a^3b} = \frac{1}{2} \cdot \frac{b^6}{a^3} = \frac{b^6}{2a^3} $

But wait — this seems to be an algebraic expression, not a number. However, the instruction says "write the answer in standard form" and then use it to color a picture, implying that the answers should be numbers.

So perhaps some of these are meant to be evaluated numerically? Let's check if there are any numerical values hidden.

Wait — let’s re-express them carefully.

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Actually, looking at the format, many of these seem to be scientific notation expressions with variables, but some might be purely numerical.

Let me re-analyze each one assuming they are expressions in scientific notation or simplified exponential forms.

But given the structure, e.g., “(6a)⁵”, “x⁻²y⁴”, etc., it appears most are algebraic expressions. But since the final output is supposed to be a number for coloring, maybe the expressions are meant to be evaluated numerically?

Alternatively, perhaps the variables represent digits? That doesn’t make sense.

Another possibility: the numbers are written in scientific notation, and the letters are just placeholders?

Wait — look at Problem 1:
8a⁰b⁷ / 16a³b

This is likely not scientific notation — it's algebraic.

But the instruction says: "Solve the following problems. Find the answer key on the page. Select the answer (in the correct standard form from that answer key)"

So perhaps there is a separate answer key that maps simplified expressions to numbers?

But since we don’t have the key or the picture, we need to simplify each expression algebraically and see if it reduces to a number.

Let’s try again, interpreting each as a mathematical expression and simplifying.

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1.) $ \frac{8a^0b^7}{16a^3b} $

- $ a^0 = 1 $
- So: $ \frac{8 \cdot 1 \cdot b^7}{16a^3b} = \frac{8b^7}{16a^3b} = \frac{1}{2} \cdot \frac{b^6}{a^3} = \frac{b^6}{2a^3} $

→ Not a number unless values are given.

Hmm. This suggests either:
- There’s missing context (like variable values), or
- The expressions are meant to be interpreted as scientific notation with "a" and "b" being digits?

Wait — look at Problem 1:
"8a⁰b⁷ / 16a³b" — perhaps this is not algebra, but scientific notation written in a confusing way?

Wait — maybe the "a" and "b" are actually digits? For example, maybe "a" stands for 10? That doesn't help.

Alternatively, could this be a typo?

Let’s look at Problem 2:
"11a⁴ · 3a⁴"

That’s clearly algebraic: $ 11a^4 \cdot 3a^4 = 33a^8 $

Again, not a number.

But the goal is to get a number to match to a color.

So perhaps all variables are equal to 1? Or maybe this is a code where a=10, b=100, etc.? That seems unlikely.

Wait — another idea: The expressions are in scientific notation, but written with "a" and "b" as placeholders for powers of 10?

For example, maybe "a" means ×10¹, "b" means ×10²?

But that’s speculative.

Alternatively, maybe the letters are digits, like in cryptarithmetic puzzles?

But without more info, that’s hard.

Wait — look at Problem 10:
"-10x⁴y⁻² · 3xy⁶"

Still algebraic.

But Problem 13:
"(-12a⁰)8b⁰"

Ah! Here, $ a^0 = 1 $, $ b^0 = 1 $, so:
$ (-12 \cdot 1) \cdot 8 \cdot 1 = -12 \cdot 8 = -96 $

That’s a number!

Similarly, Problem 15:
"5⁻²a⁰b⁻⁹"

- $ 5^{-2} = \frac{1}{25} $
- $ a^0 = 1 $
- $ b^{-9} = \frac{1}{b^9} $ → still depends on b

Unless b is defined.

But in Problem 13, it worked because only constants were involved.

Let’s go through all problems again, assuming that any variable raised to power 0 is 1, and if no other value is given, maybe variables are meant to be 1? Or perhaps only when they appear in a way that cancels?

But that’s not consistent.

Wait — perhaps the expressions are meant to be simplified using exponent rules, and the final answer is a number, meaning that all variables are equal to 1?

Let’s assume a = 1, b = 1, x = 1, y = 1, z = 1, unless otherwise specified.

That would make sense for a coloring activity.

Let’s test that.

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Assumption: All variables (a, b, x, y, z) are equal to 1.

Then simplify each expression numerically.

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1.) $ \frac{8a^0b^7}{16a^3b} $

- $ a^0 = 1 $, $ b^7 = 1^7 = 1 $, $ a^3 = 1 $, $ b = 1 $
- Numerator: $ 8 \cdot 1 \cdot 1 = 8 $
- Denominator: $ 16 \cdot 1 \cdot 1 = 16 $
- Result: $ 8/16 = 0.5 $

→ 0.5

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2.) $ 11a^4 \cdot 3a^4 $

- $ a^4 = 1 $
- $ 11 \cdot 1 \cdot 3 \cdot 1 = 33 $

→ 33

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3.) $ 13c^{-7}d $

- $ c^{-7} = 1/c^7 = 1/1 = 1 $, $ d = 1 $
- $ 13 \cdot 1 \cdot 1 = 13 $

→ 13

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4.) $ (6a)^5 $

- $ 6a = 6 \cdot 1 = 6 $
- $ 6^5 = 7776 $

→ 7776

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5.) $ (8y)^0 $

- Any non-zero number to the 0 power is 1
- $ 8y = 8 \cdot 1 = 8 \neq 0 $
- So $ (8y)^0 = 1 $

→ 1

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6.) $ \frac{5 \cdot c \cdot d^{11}}{8 \cdot d \cdot c^{-8}} $

- $ c = 1 $, $ d = 1 $
- Numerator: $ 5 \cdot 1 \cdot 1^{11} = 5 $
- Denominator: $ 8 \cdot 1 \cdot 1^{-8} = 8 \cdot 1 = 8 $
- $ 5/8 = 0.625 $

→ 0.625

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7.) $ x^{-2}y^4 $

- $ x^{-2} = 1/x^2 = 1/1 = 1 $, $ y^4 = 1 $
- $ 1 \cdot 1 = 1 $

→ 1

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8.) $ 7cd^9 \cdot 4cd^3 $

- $ c = 1 $, $ d = 1 $
- $ 7 \cdot 1 \cdot 1^9 = 7 $, $ 4 \cdot 1 \cdot 1^3 = 4 $
- Multiply: $ 7 \cdot 4 = 28 $

→ 28

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9.) $ (9a \cdot 6) \cdot 7^3 $

- $ 9a = 9 \cdot 1 = 9 $
- $ 9 \cdot 6 = 54 $
- $ 7^3 = 343 $
- $ 54 \cdot 343 $

Calculate:
- $ 50 \cdot 343 = 17,150 $
- $ 4 \cdot 343 = 1,372 $
- Total: $ 17,150 + 1,372 = 18,522 $

→ 18,522

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10.) $ -10x^4y^{-2} \cdot 3xy^6 $

- $ x^4 = 1 $, $ y^{-2} = 1 $, $ x = 1 $, $ y^6 = 1 $
- $ -10 \cdot 1 \cdot 1 \cdot 3 \cdot 1 \cdot 1 = -30 $

→ -30

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11.) $ \frac{3y^{12} \cdot 5}{27x^3y^1z} $

- $ y^{12} = 1 $, $ y^1 = 1 $, $ x^3 = 1 $, $ z = 1 $
- Numerator: $ 3 \cdot 1 \cdot 5 = 15 $
- Denominator: $ 27 \cdot 1 \cdot 1 \cdot 1 = 27 $
- $ 15/27 = 5/9 \approx 0.555... $

→ 5/9 or 0.555...

But likely keep as fraction: 5/9

But for coloring, probably decimal or whole number.

Wait — maybe reduce: $ \frac{15}{27} = \frac{5}{9} $

→ 5/9

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12.) $ -(4x)^0 \cdot 5y^0 $

- $ (4x)^0 = 1 $ (since 4x ≠ 0)
- $ y^0 = 1 $
- So: $ -1 \cdot 5 \cdot 1 = -5 $

→ -5

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13.) $ (-12a^0) \cdot 8b^0 $

- $ a^0 = 1 $, $ b^0 = 1 $
- $ -12 \cdot 1 = -12 $
- $ -12 \cdot 8 = -96 $

→ -96

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14.) $ (-12xy) \cdot 3 $

- $ x = 1 $, $ y = 1 $
- $ -12 \cdot 1 \cdot 1 = -12 $
- $ -12 \cdot 3 = -36 $

→ -36

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15.) $ 5^{-2}a^0b^{-9} $

- $ 5^{-2} = 1/25 $
- $ a^0 = 1 $
- $ b^{-9} = 1/b^9 = 1/1 = 1 $
- So: $ (1/25) \cdot 1 \cdot 1 = 1/25 = 0.04 $

→ 0.04

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Now let’s compile all answers:

| Problem | Answer |
|--------|--------|
| 1 | 0.5 |
| 2 | 33 |
| 3 | 13 |
| 4 | 7776 |
| 5 | 1 |
| 6 | 0.625 |
| 7 | 1 |
| 8 | 28 |
| 9 | 18,522 |
| 10 | -30 |
| 11 | 5/9 ≈ 0.555... |
| 12 | -5 |
| 13 | -96 |
| 14 | -36 |
| 15 | 0.04 |

Now, since the instruction says to match to a color code, and you're to color the picture, these numbers must correspond to colors in a provided key.

Since we don’t have the key, we can’t assign colors.

But the solution is:

> Simplify each expression, assuming all variables equal 1 (since no values are given), and compute the numeric result.

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✔ Final Answers (Standard Form):

1. 0.5
2. 33
3. 13
4. 7776
5. 1
6. 0.625
7. 1
8. 28
9. 18,522
10. -30
11. 5/9 or ≈0.555...
12. -5
13. -96
14. -36
15. 0.04

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📌 Explanation:

- We assumed all variables (a, b, x, y, z) are equal to 1, as no values were provided.
- Used exponent rules: $ x^0 = 1 $, $ x^{-n} = 1/x^n $
- Simplified each expression algebraically first, then substituted values.
- Reduced fractions and decimals as needed.
- These numeric answers should match a color key (not shown) to determine which color to use for each part of the picture.

If you can provide the answer key or the picture grid, I can help match the colors.

Otherwise, this is the complete solution to the mathematical part of the problem.