Question

How do you simplify ${{\left( \dfrac{3}{5} \right)}^{-2}}$?

Answer 1

Hint: As the given exponent is the negative exponent. To solve the negative exponent we need to change the sign from negative to positive. First we will change the sign by taking the reciprocal of the given fraction and then solve further to get the desired answer.

Complete step by step answer:
We have to simplify the given fraction ${{\left( \dfrac{3}{5} \right)}^{-2}}$.
Now, we know that the negative exponent rule says that the negative exponent in the numerator gets moved to the denominator and becomes positive exponent. Similarly negative exponents in the denominator get moved to the numerator and become positive exponents.
Now, to make the given fraction exponent positive we need to take the reciprocal of it. Then we will get
$\begin{align}
  & \Rightarrow {{\left( \dfrac{3}{5} \right)}^{-2}} \\
 & \Rightarrow {{\left( \dfrac{5}{3} \right)}^{2}} \\
\end{align}$
Now, we know that the exponent of a number says how many times to use a number in multiplication. Here in this question we have given the exponent 2 so we need to multiply the given numbers two times.
Then we will get
$\Rightarrow \left( \dfrac{5\times 5}{3\times 3} \right)$
Now, simplifying the above obtained equation we get
$\Rightarrow \dfrac{25}{9}$

So on solving the given fraction ${{\left( \dfrac{3}{5} \right)}^{-2}}$ we get the value $\dfrac{25}{9}$.

Note: The exponent of a number says how many times to use a number in multiplication. A positive exponent says how many times a number is used in the multiplication. A negative exponent means how many times to divide by the number. Be careful while taking the reciprocal of the given fraction.