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Simplify. Express your answer using a single exponent.\newline(9k5)2(9k^5)^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(9k5)2(9k^5)^2
  1. Apply Power Rule: Apply the power to a power rule.\newlineWhen raising a power to another power, we multiply the exponents. For the base 99, which is a constant, we simply square it. For the variable kk raised to the 55th power, we multiply the exponents.\newline(9k5)2=92×(k5)2(9k^5)^2 = 9^2 \times (k^5)^2
  2. Calculate 929^2: Calculate 929^2. \newline92=9×9=819^2 = 9 \times 9 = 81
  3. Calculate (k5)2(k^5)^2: Calculate (k5)2(k^5)^2.(k5)2=k(5×2)=k10(k^5)^2 = k^{(5 \times 2)} = k^{10}
  4. Combine Results: Combine the results from Step 22 and Step 33. 81×k10=81k1081 \times k^{10} = 81k^{10}

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