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.