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Simplify. Express your answer using a single exponent.\newline(4k9)2(4k^9)^2

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Powers of a power: variable basesright chevron icon

Full solution

Q. Simplify. Express your answer using a single exponent.\newline(4k9)2(4k^9)^2
  1. Apply Power to Coefficient and Variable: Apply the power to both the coefficient and the variable.\newlineWhen raising a power to a power, we multiply the exponents, and when raising a coefficient to a power, we simply calculate the power of the number.\newline(4k9)2=42×(k9)2(4k^9)^2 = 4^2 \times (k^9)^2
  2. Calculate Power of Coefficient: Calculate the power of the coefficient. 42=4×4=164^2 = 4 \times 4 = 16
  3. Calculate Power of Variable: Calculate the power of the variable.\newline(k9)2=k(9×2)=k18(k^9)^2 = k^{(9 \times 2)} = k^{18}
  4. Combine Results: Combine the results to express the final answer.\newline(4k9)2=16×k18=16k18(4k^9)^2 = 16 \times k^{18} = 16k^{18}

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