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Simplify. Express your answer using a single exponent.\newline(2k8)4(2k^8)^4

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(2k8)4(2k^8)^4
  1. Apply Power Rule: Apply the power rule to the expression (2k8)4(2k^8)^4. The power rule states that when raising a power to another power, you multiply the exponents. For the coefficient 22, which is raised to the power of 11 implicitly, we will also apply the power rule. (2k8)4=24×(k8)4(2k^8)^4 = 2^4 \times (k^8)^4
  2. Calculate 242^4: Calculate 242^4.\newline24=2×2×2×2=162^4 = 2 \times 2 \times 2 \times 2 = 16
  3. Calculate (k8)4(k^8)^4: Calculate (k8)4(k^8)^4.(k8)4=k(8×4)=k32(k^8)^4 = k^{(8 \times 4)} = k^{32}
  4. Combine Results: Combine the results from Step 22 and Step 33.\newline(2k8)4=24×k32=16k32(2k^8)^4 = 2^4 \times k^{32} = 16k^{32}

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