Question

Evaluate the value of the following:

$\frac{9^2\times 8^2}{72}$

Answer 1

Hint: As we know the following laws of exponents is:

1. $x^a\times x^b=x^{a+b}$
2. ${(x\times y)}^a=x^a\times y^a$
3. $\frac{x^a}{x^b}=x^{a-b}$

Step 1: Given number: $\frac{9^2\times 8^2}{72}$

Step2: Solution:

Using the above law of exponents:

$$\begin{gathered} \frac{9^2\times 8^2}{72}=\frac{9^2\times 8^2}{9\times 8} \\ =9^{2-1}\times 8^{2-1}\left\{U\sin g\frac{x^a}{x^b}=x^{a-b}\right\} \\ =9\times 8=72 \end{gathered}$$

$72$, This is the required value.

Final Answer: $72$, This is the required value.