Question

simplify: [9(27⅓ + 216⅓)³]¼​

Answer 1

Answer:

9

Step-by-step explanation:

[9(3+6)^3]^(1/4)

[9^(1+3)]^(1/4)

(9^4)^(1/4)

9

Answer 2

$\huge\fcolorbox{red}{cyan}{9}$

Step-by-step explanation:

Laws Of Exponent :-

• $\bf\color{purple}{(x^a)^b = x^{ab}}$
• $\bf\color{orange}{(a)^\frac{1}{x}}=\sqrt[x]{a}$

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Lets Put the values :-

$[9(27^{\frac{1}{3}} + 216^{\frac{1}{3}})^3] ^ {\frac{1}{4}} \\ =>\bf{Applying\:Law\:Of\:Exponent} \\ => [9(\sqrt[3]{27}+\sqrt[3]{216})^{\frac{1}{3}}]^\frac{1}{4} \\ => [9(3+6)^3]^{\frac{1}{4}} \\ => (9 \times 9^3)^{\frac{1}{4}} \\ => (9^4)^{\frac{1}{4}} \\ => 9 ^ {4 \times \frac{1}{4}} \\ => \boxed{9}$

Hope it helped.