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Simplify. Express your answer using a single exponent.\newline(4y5)3(4y^5)^3

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(4y5)3(4y^5)^3
  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 33.\newline(4y5)3=43×(y5)3(4y^5)^3 = 4^3 \times (y^5)^3
  2. Calculate 434^3: Calculate 434^3.\newline43=4×4×4=644^3 = 4 \times 4 \times 4 = 64
  3. Calculate (y5)3(y^5)^3: Calculate (y5)3(y^5)^3.(y5)3=y(5×3)=y15(y^5)^3 = y^{(5 \times 3)} = y^{15}
  4. Combine Results: Combine the results from Step 22 and Step 33.\newline(4y5)3=43×(y5)3=64×y15(4y^5)^3 = 4^3 \times (y^5)^3 = 64 \times y^{15}
  5. Write Final Expression: Write the final simplified expression.\newlineThe expression (4y5)3(4y^5)^3 simplifies to 64y1564y^{15}.

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