Question

By what number should be (5/4)^-2 be divided, so that the quotient (1/2)^-3?​

Answer 1

let the no. be x

=(5/4)-²/x=(1/2) -³

=(4/5)²/x=(2/1)³

=(4/5)²= x *(2/1)³

=(16/25)= x*(8/1)

=(16/25)x(1/8)=x

=x =2/25 is the no.

Answer 2

We need to divide by 2/25.

Step-by-step explanation:

In order to find by which number the expression (5/4)^-2 should be divided to get the quotient (1/2)^-3, we'll perform the below operation:

Divide  (5/4)^-2 by (1/2)^-3

$\frac{(\frac{5}{4})^{-2}}{(\frac{1}{2})^{-3}}$

Apply the exponent rule: $(\frac{x}{y})^{-a}=(\frac{y}{x})^a$

$\frac{(\frac{4}{5})^{2}}{(2)^{3}}$

On simplifying, we get

$\frac{\frac{16}{25}}{8}\\\\=\frac{16}{25\cdot8}\\\\=\frac{2}{25}$

So, we need to divide by 2/25.

#Learn More:

By what number should (-3/2)-3 be divided so that the quotient is (9/4)-2

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