Question

Simplify [5(8*1/3+27*1/3)*3]*1/4

Answer 1

Answer:

5

Explanation:

Given [5(8⅓ + 27⅓)³]¼

= {5[(2³)⅓+(3³)⅓]³}¼

$\boxed {(a^{m})^{n} = a^{mn}}$

= [5(2+3)³]¼

= [5×5³]¼

$\boxed { a^{m} \times a^{n} = a^{m+n}}$

= [5⁴]¼

=5

Therefore,

[5(8⅓ + 27⅓)³]¼ = 5

••••

Answer 2

$\underline{\textbf{Given:}}$

$\mathsf{[5(8^\frac{1}{3}+27^\frac{1}{3})^3]^\frac{1}{4}}$

$\underline{\textbf{To simplify:}}$

$\mathsf{[5(8^\frac{1}{3}+27^\frac{1}{3})^3]^\frac{1}{4}}$

$\underline{\textbf{Solution:}}$

$\underline{\textsf{Concept used:}}$

$\mathsf{*\;(a^m)^n=a^{mn}}$

$\mathsf{*\;a^ma^n=a^{m+n}}$

$\mathsf{Consider,}$

$\mathsf{[5(8^\frac{1}{3}+27^\frac{1}{3})^3]^\frac{1}{4}}$

$\mathsf{=[5((2^3)^\frac{1}{3}+(3^3)^\frac{1}{3})^3]^\frac{1}{4}}$

$\mathsf{=[5(2^{3\times\frac{1}{3}}+3^{3\times\frac{1}{3}})^3]^\frac{1}{4}}$

$\mathsf{=[5(2^1+3^1)^3]^\frac{1}{4}}$

$\mathsf{=[5(2+3)^3]^\frac{1}{4}}$

$\mathsf{=[5(5)^3]^\frac{1}{4}}$

$\mathsf{=[5^1(5)^3]^\frac{1}{4}}$

$\mathsf{=[5^4]^\frac{1}{4}}$

$\mathsf{=5^{4\times\frac{1}{4}}}$

$\mathsf{=5^1}$

$\mathsf{=5}$

$\underline{\textbf{Find more:}}$

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