Simplify ((4^2)^3)/((7^3)^2)

$\frac{{(4^{2})}^{3}}{{(7^{3})}^{2}}$

Step 1

Simplify the numerator.

Multiply the exponents in ${(4^{2})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{4^{2 \cdot 3}}{{(7^{3})}^{2}}$

Multiply $2$ by $3$ .

$\frac{4^{6}}{{(7^{3})}^{2}}$

Raise $4$ to the power of $6$ .

$\frac{4096}{{(7^{3})}^{2}}$

Step 2

Simplify the denominator.

Multiply the exponents in ${(7^{3})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{4096}{7^{3 \cdot 2}}$

Multiply $3$ by $2$ .

$\frac{4096}{7^{6}}$

Raise $7$ to the power of $6$ .

$\frac{4096}{117649}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{4096}{117649}$

Decimal Form:

$0.03481542 \dots$