Question

( 64/729) is power to -1/6 what is its simplest form?

Answer 1

Answer:

3/2

Step-by-step explanation:

please mark as Brainliest

Answer 2

Answer:

The value of    $(\frac{64}{729} )^{\frac{-1}{6} }$ = $\frac{3}{2}$

Step-by-step explanation:

Given that (64/729)$^{\frac{-1}{6} }$

We have to find the simplest form of given expression.

64 = 2 × 2× 2× 2× 2× 2 = 2⁶

729 = 3× 3 × 3× 3× 3 × 3 = 3⁶

We know that$(\frac{a}{b} )^{n} =\frac{a^{n} }{b^{n} }$

Now the expression becomes,

$(\frac{64}{729} )^{\frac{-1}{6} }$= $\frac{(64)^{\frac{-1}{6} } }{(729)^{\frac{-1}{6} } }$ = $\frac{(2^{6})^{\frac{-1}{6} } }{(3^{6})^{\frac{-1}{6} } } =\frac{(2)^{-1} }{(3)^{-1} } = \frac{\frac{1}{2} }{\frac{1}{3} } =3(\frac{1}{2} )=\frac{3}{2}$

Therefore,  $(\frac{64}{729} )^{\frac{-1}{6} }$ = $\frac{3}{2}$