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The value of \(\left[5{\left(8^{\frac{1}{3}}+27^{\frac{1}{3}}\right)^3}\right]^{\frac{1}{4}}\) is
1. 5
2. 52
3. 53
4. 54

1 Answer

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Best answer
Correct Answer - Option 1 : 5

Formula used:

(ax)y = axy

Calculation:

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

⇒ \(\left[5{\left((2^3)^{\frac{1}{3}}+(3^3)^{\frac{1}{3}}\right)^3}\right]^{\frac{1}{4}}\)

⇒ \(\left[5{\left((2)+(3)\right)^3}\right]^{\frac{1}{4}}\)

⇒ \(\left[5{\left(2 + 3\right)^3}\right]^{\frac{1}{4}}\) 

⇒ \(\left[5 ×{\left(5\right)^3}\right]^{\frac{1}{4}}\)

⇒ \(\left[{\left(5\right)^4}\right]^{\frac{1}{4}}\) = 5

∴ The value of \(\left[5{\left(8^{\frac{1}{3}}+27^{\frac{1}{3}}\right)^3}\right]^{\frac{1}{4}}\) is 5.

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