Question

by what no. should (5/4) raised to power -2 be divided so that the quotient is (1/2) raised to power -3​

Answer 1

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

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

Apply the exponent rule:

$(\frac{x}{y})^{-a}=(\frac{y}{x})^a$

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

On simplifying, we get

$\begin{gathered}\frac{\frac{16}{25}}{8}\\\\=\frac{16}{25 \times 8}\\\\=\frac{2}{25}\end{gathered}$

So, we need to divide by 2/25.