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Simplify. Express your answer using a single exponent.\newline(9g5)2(9g^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(9g5)2(9g^5)^2
  1. Apply Power Rule: Apply the power to a power rule.\newlineWe need to distribute the exponent 22 to both the base 99 and the exponent of g5g^5.\newline(9g5)2=92×(g5)2(9g^5)^2 = 9^2 \times (g^5)^2
  2. Simplify 929^2: Simplify 929^2.\newlineCalculate the square of 99.\newline92=9×9=819^2 = 9 \times 9 = 81
  3. Simplify (g5)2(g^5)^2: Simplify (g5)2(g^5)^2.\newlineApply the power to a power rule by multiplying the exponents.\newline(g5)2=g(5×2)=g10(g^5)^2 = g^{(5 \times 2)} = g^{10}
  4. Combine Results: Combine the results from Step 22 and Step 33.\newlineMultiply the simplified base and exponent together.\newline(9g5)2=81×g10(9g^5)^2 = 81 \times g^{10}

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