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Simplify. Express your answer using a single exponent.\newline(9z7)2(9z^7)^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(9z7)2(9z^7)^2
  1. Apply Power Rule: Apply the power to a power rule.\newlineWhen raising a power to another power, we multiply the exponents. We also raise the numerical coefficient to the power of 22.\newline(9z7)2=92×(z7)2(9z^7)^2 = 9^2 \times (z^7)^2
  2. Calculate 929^2: Calculate 929^2. \newline92=9×9=819^2 = 9 \times 9 = 81
  3. Calculate (z7)2(z^7)^2: Calculate (z7)2(z^7)^2.(z7)2=z(7×2)=z14(z^7)^2 = z^{(7 \times 2)} = z^{14}
  4. Combine Results: Combine the results from Step 22 and Step 33.\newline(9z7)2=81×z14(9z^7)^2 = 81 \times z^{14}

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