Since the user options (ExplainAnswer, TeachTopic, GeneratePractice) are all set to false, I will only provide the final answers for each problem as listed in the image, verified step by step.
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Problem 1:
$4x^3 \cdot 2x^3$
Multiply coefficients: $4 \cdot 2 = 8$
Add exponents: $x^{3+3} = x^6$
→ Final: $8x^6$
✔
Problem 2:
$x^5 \cdot x^3$
Add exponents: $x^{5+3} = x^8$
→ Final: $x^8$
✔
Problem 3:
$2x^3 \cdot 2x^2$
Multiply coefficients: $2 \cdot 2 = 4$
Add exponents: $x^{3+2} = x^5$
→ Final: $4x^5$
✔
Problem 4:
$\frac{6^5}{6^3}$
Subtract exponents: $6^{5-3} = 6^2 = 36$
→ Final: $36$
✔
Problem 5:
$\frac{x^4}{x^7}$
Subtract exponents: $x^{4-7} = x^{-3} = \frac{1}{x^3}$
→ Final: $\frac{1}{x^3}$
✔
Problem 6:
$8^0$
Any nonzero number to the power of 0 is 1.
→ Final: $1$
✔
Problem 7:
$\frac{6x^7}{2x^4}$
Divide coefficients: $6 ÷ 2 = 3$
Subtract exponents: $x^{7-4} = x^3$
→ Final: $3x^3$
✔
Problem 8:
$\frac{x^2 y^5}{x y^4}$
For x: $x^{2-1} = x^1 = x$
For y: $y^{5-4} = y^1 = y$
→ Final: $xy$
✔
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Final Answer:
1. $8x^6$
2. $x^8$
3. $4x^5$
4. $36$
5. $\frac{1}{x^3}$
6. $1$
7. $3x^3$
8. $xy$
Parent Tip: Review the logic above to help your child master the concept of laws of exponents worksheet.
