Simplify (6^2p^4r^6)/(2^4(p^2r)^2)

$\frac{6^{2} p^{4} r^{6}}{2^{4} {(p^{2} r)}^{2}}$

Step 1

Raise $6$ to the power of $2$ .

$\frac{36 p^{4} r^{6}}{2^{4} {(p^{2} r)}^{2}}$

Step 2

Simplify the denominator.

Apply the product rule to $p^{2} r$ .

$\frac{36 p^{4} r^{6}}{2^{4} {(p^{2})}^{2} r^{2}}$

Raise $2$ to the power of $4$ .

$\frac{36 p^{4} r^{6}}{16 {(p^{2})}^{2} r^{2}}$

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

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

$\frac{36 p^{4} r^{6}}{16 p^{2 \cdot 2} r^{2}}$

Multiply $2$ by $2$ .

$\frac{36 p^{4} r^{6}}{16 p^{4} r^{2}}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $36$ and $16$ .

Factor $4$ out of $36 p^{4} r^{6}$ .

$\frac{4 (9 p^{4} r^{6})}{16 p^{4} r^{2}}$

Cancel the common factors.

Factor $4$ out of $16 p^{4} r^{2}$ .

$\frac{4 (9 p^{4} r^{6})}{4 (4 p^{4} r^{2})}$

Cancel the common factor.

$\frac{4 (9 p^{4} r^{6})}{4 (4 p^{4} r^{2})}$

Rewrite the expression.

$\frac{9 p^{4} r^{6}}{4 p^{4} r^{2}}$

Cancel the common factor of $p^{4}$ .

Cancel the common factor.

$\frac{9 p^{4} r^{6}}{4 p^{4} r^{2}}$

Rewrite the expression.

$\frac{9 r^{6}}{4 r^{2}}$

Cancel the common factor of $r^{6}$ and $r^{2}$ .

Factor $r^{2}$ out of $9 r^{6}$ .

$\frac{r^{2} (9 r^{4})}{4 r^{2}}$

Cancel the common factors.

Factor $r^{2}$ out of $4 r^{2}$ .

$\frac{r^{2} (9 r^{4})}{r^{2} \cdot 4}$

Cancel the common factor.

$\frac{r^{2} (9 r^{4})}{r^{2} \cdot 4}$

Rewrite the expression.

$\frac{9 r^{4}}{4}$