Question

If x=(5/8)^-2×(12/15)^-2 then find the value of x^2 and x^-2 respectively

Answer 1

Step-by-step explanation:

Here is your  answer:

Given that,

x = (\frac{5}{8})^{-2} ( \frac{12}{15})^{-2}x=(85)−2(1512)−2 

To find,

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

Solution:

We know that,  

a^{-n}= (\frac{1}{a})^{n}a−n=(a1)n     --- (Identity)

Then,

x = (\frac{5}{8})^{-2} \times ( \frac{12}{15})^{-2} = ( \frac{8}{5})^{2} \times ( \frac{15}{12})^{2}x=(85)−2×(1512)−2=(58)2×(1215)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 = 4x=5×58×8×12×1215×15=1×12×2×3×33×3=2×2=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}x−3=x31=431=4×4×41=641 

HOPE THIS HELPS