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Write in exponential notation: ((n^(4))^(5))^(2)

Write in exponential notation:\newline((n4)5)2 \left(\left(n^{4}\right)^{5}\right)^{2}

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Full solution

Q. Write in exponential notation:\newline((n4)5)2 \left(\left(n^{4}\right)^{5}\right)^{2}
  1. Apply Exponent Rule: We need to simplify the expression ((n4)5)2((n^{4})^{5})^{2} using the property of exponents that states (am)n=am∗n(a^{m})^{n} = a^{m*n}.
  2. Simplify Innermost Expression: First, apply the exponent rule to the innermost expression: (n4)5(n^{4})^{5}.(n4)5=n4∗5=n20(n^{4})^{5} = n^{4*5} = n^{20}.
  3. Apply Exponent Rule Again: Now, apply the exponent rule to the resulting expression with the outer exponent: (n20)2(n^{20})^2.(n20)2=n20∗2=n40(n^{20})^2 = n^{20*2} = n^{40}.
  4. Final Simplification: We have simplified the expression to n40n^{40}, which is in exponential notation.

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