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Simplify. Express your answer using a single exponent.\newline(2j8)3(2j^8)^3

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(2j8)3(2j^8)^3
  1. Apply Power Rule: Apply the power to a power rule.\newlineWhen raising a power to another power, we multiply the exponents. For the expression (2j8)3(2j^8)^3, we apply this rule to the jj term.\newline(2j8)3=23×(j8)3(2j^8)^3 = 2^3 \times (j^8)^3
  2. Calculate 232^3: Calculate 232^3.\newline23=2×2×2=82^3 = 2 \times 2 \times 2 = 8
  3. Calculate (j8)3(j^8)^3: Calculate (j8)3(j^8)^3.(j8)3=j(8×3)=j24(j^8)^3 = j^{(8 \times 3)} = j^{24}
  4. Combine Results: Combine the results from Step 22 and Step 33.\newline(2j8)3=23×(j8)3=8×j24(2j^8)^3 = 2^3 \times (j^8)^3 = 8 \times j^{24}
  5. Write Final Expression: Write the final simplified expression.\newlineThe expression (2j8)3(2j^8)^3 simplifies to 8j248j^{24}.

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