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Simplify. Express your answer using a single exponent.\newline(4y7)2(4y^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(4y7)2(4y^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(4y7)2=42×(y7)2(4y^7)^2 = 4^2 \times (y^7)^2
  2. Calculate 424^2: Calculate 424^2. \newline42=4×4=164^2 = 4 \times 4 = 16
  3. Calculate (y7)2(y^7)^2: Calculate (y7)2(y^7)^2.(y7)2=y(7×2)=y14(y^7)^2 = y^{(7 \times 2)} = y^{14}
  4. Combine results: Combine the results from Step 22 and Step 33.\newline(4y7)2=16×y14(4y^7)^2 = 16 \times y^{14}

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