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Simplify. Express your answer using a single exponent.\newline(6g5)3(6g^5)^3

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(6g5)3(6g^5)^3
  1. Apply Power Rule: 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 raise the number to that power.\newline(6g5)3=63×(g5)3(6g^5)^3 = 6^3 \times (g^5)^3
  2. Calculate 636^3: Calculate 636^3.\newline63=6×6×6=2166^3 = 6 \times 6 \times 6 = 216
  3. Calculate (g5)3(g^5)^3: Calculate (g5)3(g^5)^3. When raising a power to another power, we multiply the exponents. (g5)3=g(5×3)=g15(g^5)^3 = g^{(5 \times 3)} = g^{15}
  4. Combine Results: Combine the results from Step 22 and Step 33.\newline(6g5)3=63×(g5)3=216×g15(6g^5)^3 = 6^3 \times (g^5)^3 = 216 \times g^{15}

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