Let's solve each problem on the
Exponent Rules Review Worksheet step by step, applying exponent rules and simplifying so that
only positive exponents appear in the final answers.
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1) $ 2x^3 \cdot 4x^2 $
- Multiply coefficients: $ 2 \cdot 4 = 8 $
- Add exponents of like bases (same base $ x $): $ x^{3+2} = x^5 $
- Result: $ \boxed{8x^5} $
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2) $ 4xy^4 \cdot x^4y^2 $
- Multiply coefficients: $ 4 \cdot 1 = 4 $
- Combine $ x $ terms: $ x \cdot x^4 = x^{1+4} = x^5 $
- Combine $ y $ terms: $ y^4 \cdot y^2 = y^{4+2} = y^6 $
- Result: $ \boxed{4x^5y^6} $
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3) $ a^0b^3 \cdot 3ab^3 $
- Recall: $ a^0 = 1 $, so this becomes $ 1 \cdot b^3 \cdot 3ab^3 = 3ab^3 \cdot b^3 $
- Multiply coefficients: $ 3 $
- Combine $ a $: $ a $
- Combine $ b $: $ b^3 \cdot b^3 = b^{3+3} = b^6 $
- Result: $ \boxed{3ab^6} $
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4) $ 2yx^2 \cdot 2x^4y^4 $
- Multiply coefficients: $ 2 \cdot 2 = 4 $
- Combine $ x $: $ x^2 \cdot x^4 = x^{2+4} = x^6 $
- Combine $ y $: $ y \cdot y^4 = y^{1+4} = y^5 $
- Result: $ \boxed{4x^6y^5} $
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5) $ ab^{-4} \cdot 2a $
- Multiply coefficients: $ 1 \cdot 2 = 2 $
- Combine $ a $: $ a \cdot a = a^2 $
- $ b^{-4} $ stays for now
- So: $ 2a^2b^{-4} $
- Convert negative exponent to positive: $ b^{-4} = \frac{1}{b^4} $
- Final answer: $ \boxed{\frac{2a^2}{b^4}} $
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6) $ 4u^{-4} \cdot uv^2 $
- Multiply coefficients: $ 4 \cdot 1 = 4 $
- Combine $ u $: $ u^{-4} \cdot u = u^{-4+1} = u^{-3} $
- $ v^2 $ remains
- So: $ 4u^{-3}v^2 $
- Convert $ u^{-3} $ to $ \frac{1}{u^3} $
- Final answer: $ \boxed{\frac{4v^2}{u^3}} $
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7) $ (4m^2n^3)^3 $
- Apply power to each part inside parentheses:
- $ 4^3 = 64 $
- $ (m^2)^3 = m^{2\cdot3} = m^6 $
- $ (n^3)^3 = n^{3\cdot3} = n^9 $
- Result: $ \boxed{64m^6n^9} $
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8) $ (4uv)^2 $
- Apply square to each part:
- $ 4^2 = 16 $
- $ u^2 $
- $ v^2 $
- Result: $ \boxed{16u^2v^2} $
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9) $ (xy^2)^2 $
- Apply square to each part:
- $ x^2 $
- $ (y^2)^2 = y^{2\cdot2} = y^4 $
- Result: $ \boxed{x^2y^4} $
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10) $ \frac{3x^4y^3}{2xy} $
- Divide coefficients: $ \frac{3}{2} $
- Divide $ x $: $ \frac{x^4}{x} = x^{4-1} = x^3 $
- Divide $ y $: $ \frac{y^3}{y} = y^{3-1} = y^2 $
- Result: $ \boxed{\frac{3}{2}x^3y^2} $
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✔ Final Answers:
1) $ 8x^5 $
2) $ 4x^5y^6 $
3) $ 3ab^6 $
4) $ 4x^6y^5 $
5) $ \frac{2a^2}{b^4} $
6) $ \frac{4v^2}{u^3} $
7) $ 64m^6n^9 $
8) $ 16u^2v^2 $
9) $ x^2y^4 $
10) $ \frac{3}{2}x^3y^2 $
All answers contain
only positive exponents, as required.
Parent Tip: Review the logic above to help your child master the concept of basic exponent rules worksheet.
