Question

Evaluate the value of the following:

$\frac{7^4\times 6^4}{{\left(42\right)}^2}$

Answer 1

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

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

Step 1: Given number: $\frac{7^4\times 6^4}{{\left(42\right)}^2}$

Step2: Solution:

Using the above law of exponents:

$$\begin{gathered} \frac{7^4\times 6^4}{{\left(42\right)}^2}=\frac{7^4\times 6^4}{{(7\times 6)}^2} \\ =\frac{7^4\times 6^4}{7^2\times 6^2}\left\{U\sin g{(x\times y)}^a=x^a\times y^a\right\} \\ =7^{4-2}\times 6^{4-2}\left\{U\sin g\frac{x^a}{x^b}=x^{a-b}\right\} \\ =7^2\times 6^2 \\ =49\times 36=1764 \end{gathered}$$

$1764$, This is the required value.

Final Answer: $1764$, This is the required value.