Question

Find the value of:
(512) to the power (-2/9)
​

Answer 1

${(512)}^{ \frac{ - 2}{9} }$

512 is the cube of 8

${ ({(8)}^{3}) }^{ \frac{ - 2}{9} }$

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

$= {2}^{-2} = 1/2^2=1/4$

1/4 is your answer...

Answer 2

Hey mate...

Here is your answer;

Answer:

(512) -2/9 = 1/4

Step-by-step explanation:

Gven : Expression (512)^{-\frac{2}{9}

To find: The value of the expression?

Solution:

First we factor 512 so that we

get to convert it into the power,

512 = 2 × 2 × 2 × 2× 2× 2× 2× 2×2

512 =

$512 = {2}^9$

substitute in expression,

$(512) - \frac{2}{9} = ( {2}^{9} ) - \frac{2}{9}$

$(512) - \frac{2}{9} = (2) - \frac{2 \times 9}{9}$

$(512) - \frac{2}{9} = (2) - 2$

$(512) - \frac{2}{9} = \frac{1}{2 {}^{2} }$

$(512) - \frac{2}{9} = \frac{1}{4}$

i hope it helps you.....

peace ✌