Question

(16/81)^-3/4 simplify

Answer 1

I hope it helps you

Answer 2

Answer:

After simplification value is $\frac{27}{8}$

Step-by-step explanation:

Given term is ${ (\frac{16}{81} )}^{( - \frac{3}{4} )}$

By law of indices,we can solve this question.

${ \frac{(2 \times 2 \times 2 \times 2)}{(3 \times 3 \times 3 \times 3)} }^{( - \frac{3}{4}) } = { \frac{ {2}^{4} }{ {3}^{4} } }^{( - \frac{3}{4} )}$

$= \frac{ {2}^{ {4}^{( - \frac{3}{4}) } } }{ {3}^{ {4}^{( - \frac{3}{4}) } } } = \frac{ {2}^{ - 4 \times \frac{3}{4} } }{ {3}^{ - 4 \times \frac{3}{4} } } = \frac{ {2}^{ - 3} }{ {3}^{ - 3} } = { (\frac{2}{3} )}^{( - 3)} = {( \frac{3}{2}) }^{3} = \frac{27}{8}$

After simplification the value of simplification is $\frac{27}{8}$

Here applied formulas are

${x}^{ - y} = \frac{1}{ {x}^{y} } \\ { {x}^{y} }^{d} = {x}^{y \times d} \\ {x}^{y} = y \: times \: x \: \: is \: multiplying \: by \: x$