Question

Evaluate the value of the following:

$\frac{6^3\times 4^3}{{\left(24\right)}^2}$

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: $\frac{6^3\times 4^3}{{\left(24\right)}^2}$

Step2: Solution:

Using the above law of exponents:

$$\begin{gathered} \frac{6^3\times 4^3}{{\left(24\right)}^2}=\frac{6^3\times 4^3}{{(6\times 4)}^2} \\ =\frac{6^3\times 4^3}{6^2\times 4^2}\left\{U\sin g{(x\times y)}^a=x^a\times y^a\right\} \\ =6^{3-2}\times 4^{3-2}\left\{U\sin g\frac{x^a}{x^b}=x^{a-b}\right\} \\ =6^1\times 4^1 \\ =24 \end{gathered}$$

$24$, This is the required value.

Final Answer: $24$, This is the required value.