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Rewrite the expression in the form of 4^n. (4^2)^4

Rewrite the expression in the form of 4n4^n. (42)4(4^2)^4

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Full solution

Q. Rewrite the expression in the form of 4n4^n. (42)4(4^2)^4
  1. Apply Power Rule: Apply the power of a power rule.\newlineThe power of a power rule states that (am)n=am∗n(a^m)^n = a^{m*n}. We will apply this rule to the given expression (42)4(4^{2})^{4}.\newline(42)4=42∗4(4^{2})^{4} = 4^{2*4}
  2. Multiply Exponents: Multiply the exponents.\newlineNow we multiply the exponents 22 and 44 to simplify the expression further.\newline4(2∗4)=484^{(2*4)} = 4^{8}
  3. Write Final Answer: Write the final answer.\newlineThe expression is now simplified to a single power of 44.\newlineAnswer: 484^{8}

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