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Simplify. Express your answer using a single exponent.\newline(8k4)2(8k^4)^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(8k4)2(8k^4)^2
  1. Apply Power to Coefficient and Variable: 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 simply calculate the power of the number.\newline(8k4)2=82×(k4)2(8k^4)^2 = 8^2 \times (k^4)^2
  2. Calculate Power of Coefficient: Calculate the power of the coefficient. 82=8×8=648^2 = 8 \times 8 = 64
  3. Calculate Power of Variable: Calculate the power of the variable with the exponent.\newline(k4)2=k(4×2)=k8(k^4)^2 = k^{(4 \times 2)} = k^8
  4. Combine Results: Combine the results to express the final answer.\newline(8k4)2=64×k8=64k8(8k^4)^2 = 64 \times k^8 = 64k^8

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