Laws of Exponents | Spidey Mojo - Free Printable

Let’s go through each problem one by one, using the laws of exponents. I’ll show you how to simplify each expression step by step.

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1. 4x³ · 2x³

Multiply the numbers: 4 × 2 = 8
Multiply the variables with same base: x³ · x³ = x^(3+3) = x⁶
→ So, 8x⁶ ✔ (already correct)

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2. x⁵ · x³

Same base? Yes → add exponents: 5 + 3 = 8
→ x⁸ ✔ (already correct)

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3. 2x³ · 2x²

Numbers: 2 × 2 = 4
Variables: x³ · x² = x^(3+2) = x⁵
→ 4x⁵ ✔ (already correct)

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4. 6⁵ / 6³

Same base → subtract exponents: 5 - 3 = 2
So, 6² = 36 ✔ (already correct)

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5. x⁴ / x⁷

Same base → subtract exponents: 4 - 7 = -3
Negative exponent means flip it: x^(-3) = 1/x³
→ 1/x³ ✔ (already correct)

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6. 8⁰

Any number (except 0) to the power 0 is 1
→ 1 ✔ (already correct)

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7. (6x⁷) / (2x⁴)

Divide numbers: 6 ÷ 2 = 3
Subtract exponents for x: 7 - 4 = 3
→ 3x³ ✔ (already correct)

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8. (x²y⁵) / (xy⁴)

Break into parts:

- For x: x² / x¹ = x^(2-1) = x¹ = x
- For y: y⁵ / y = y^(5-4) = y¹ = y

Multiply them: x · y = xy ✔ (already correct)

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All answers are already correctly simplified!

Final Answer:
All given simplifications are correct as written:
1. 8x⁶
2. x⁸
3. 4x⁵
4. 36
5. 1/x³
6. 1
7. 3x³
8. xy