Mathematics: Simplify the following expression.a. 64b. 12c. 1/12d. 1/64

Simplify the following expression.a. 64b. 12c. - id6412112324136, Lindseycline123

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10.03.2022

Option D. 1/64

Step-by-step explanation:

We have to simplify the following expression

$4^{-\frac{11}{3} }$ ÷ $4^{-\frac{2}{3} }$

= $\frac{4^{-\frac{11}{3} } }{4^{-\frac{2}{3} } }$

= $[4^{-\frac{11}{3}}$ × $4^{\frac{2}{3}}]$ [since $\frac{1}{A-1}$ =a]

= $4^{(-\frac{11}{3}+\frac{2}{3})}$ [since $a^{b}$ × $a^{c}$ = $a^{(b+c)}$ ]

= $4^{-\frac{9}{3}}$

= $4^{-3}$

= $\frac{1}{4^{3} }$ [ $a^{-1}=\frac{1}{a}$ ]

= $\frac{1}{64}$

Option D. 1/64 is the answer.

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