Question

if x= (5/8)^-2 into (12/15)^-2 ,then the value of x^-3 is

Answer 1

Hi friend, Harish here.

Here is your  answer:

Given that,

$x = (\frac{5}{8})^{-2} ( \frac{12}{15})^{-2}$

To find,

$The\ value\ of \ x^{-3}$

Solution:

We know that,  

$a^{-n}= (\frac{1}{a})^{n}$    --- (Identity)

Then,

$x = (\frac{5}{8})^{-2} \times ( \frac{12}{15})^{-2} = ( \frac{8}{5})^{2} \times ( \frac{15}{12})^{2}$

⇒  $x = \frac{8\times 8}{5\times 5} \times \frac{15\times 15}{12\times 12} = \frac{2\times 2}{1\times 1} \times \frac{3\times 3}{3\times 3} = 2\times 2 = 4$

So , x = 4

Then,

$x^{-3} = \frac{1}{x^{3}} = \frac{1}{4^{3}} = \frac{1}{4\times 4\times 4} = \frac{1}{64}$

Therefore the answer is 1 / 64. 
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Hope my answer is helpful to you.

Answer 2

Step-by-step explanation:

x=(5/8)^-2*(12/15)^-2

x=(8/5)^2*(15/12)^2

x=64/25*125/144

x=4

then the value of x^-3

= 4^-3=(1/4)^3=1/64

Hope this answer is helpful to you