Question

Simplify and write $\frac{3^6\times 7^6}{{\left(21\right)}^4}$ as a single exponent.

Answer 1

We know powers get added or subtracted in multiplication or division respectively when the base is same.

So, we will identify equal bases and then solve accordingly.

In $\frac{3^6\times 7^6}{{\left(21\right)}^4}$, write $21$ as $7\times 3$ and write it as $\frac{3^6\times 7^6}{{\left(3\times 7\right)}^4}$.

After this, in $\frac{3^6\times 7^6}{{\left(3\times 7\right)}^4}$, write the exponent in common if the exponent is same and base is different, i.e., $\frac{{\left(3\times 7\right)}^6}{{\left(3\times 7\right)}^4}$.

Now, the exponents will get subtracted of the same base, i.e., ${\left(3\times 7\right)}^{6-4}={\left(3\times 7\right)}^2={\left(21\right)}^2$