Simplify (4/p)^4((4q^4)/(3p))^-2

${(\frac{4}{p})}^{4} {(\frac{4 q^{4}}{3 p})}^{- 2}$

Step 1

Apply the product rule to $\frac{4}{p}$ .

$\frac{4^{4}}{p^{4}} {(\frac{4 q^{4}}{3 p})}^{- 2}$

Step 2

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

$\frac{256}{p^{4}} {(\frac{4 q^{4}}{3 p})}^{- 2}$

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

$\frac{256}{p^{4}} {(\frac{3 p}{4 q^{4}})}^{2}$

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{3 p}{4 q^{4}}$ .

$\frac{256}{p^{4}} \cdot \frac{{(3 p)}^{2}}{{(4 q^{4})}^{2}}$

Apply the product rule to $3 p$ .

$\frac{256}{p^{4}} \cdot \frac{3^{2} p^{2}}{{(4 q^{4})}^{2}}$

Apply the product rule to $4 q^{4}$ .

$\frac{256}{p^{4}} \cdot \frac{3^{2} p^{2}}{4^{2} {(q^{4})}^{2}}$

Step 5

Simplify terms.

Combine.

$\frac{256 (3^{2} p^{2})}{p^{4} (4^{2} {(q^{4})}^{2})}$

Cancel the common factor of $p^{2}$ and $p^{4}$ .

Factor $p^{2}$ out of $256 (3^{2} p^{2})$ .

$\frac{p^{2} (256 \cdot (3^{2}))}{p^{4} (4^{2} {(q^{4})}^{2})}$

Cancel the common factors.

Factor $p^{2}$ out of $p^{4} (4^{2} {(q^{4})}^{2})$ .

$\frac{p^{2} (256 \cdot (3^{2}))}{p^{2} (p^{2} (4^{2} {(q^{4})}^{2}))}$

Cancel the common factor.

$\frac{p^{2} (256 \cdot (3^{2}))}{p^{2} (p^{2} (4^{2} {(q^{4})}^{2}))}$

Rewrite the expression.

$\frac{256 \cdot (3^{2})}{p^{2} (4^{2} {(q^{4})}^{2})}$

Raise $3$ to the power of $2$ .

$\frac{256 \cdot 9}{p^{2} \cdot 4^{2} {(q^{4})}^{2}}$

Step 6

Simplify the denominator.

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

$\frac{256 \cdot 9}{p^{2} \cdot 16 {(q^{4})}^{2}}$

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

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

$\frac{256 \cdot 9}{p^{2} \cdot 16 q^{4 \cdot 2}}$

Multiply $4$ by $2$ .

$\frac{256 \cdot 9}{p^{2} \cdot 16 q^{8}}$

Step 7

Reduce the expression by cancelling the common factors.

Multiply $256$ by $9$ .

$\frac{2304}{p^{2} \cdot 16 q^{8}}$

Cancel the common factor of $2304$ and $16$ .

Factor $16$ out of $2304$ .

$\frac{16 \cdot 144}{p^{2} \cdot 16 q^{8}}$

Cancel the common factors.

Factor $16$ out of $p^{2} \cdot 16 q^{8}$ .

$\frac{16 \cdot 144}{16 (p^{2} q^{8})}$

Cancel the common factor.

$\frac{16 \cdot 144}{16 (p^{2} q^{8})}$

Rewrite the expression.

$\frac{144}{p^{2} q^{8}}$

Simplify (4/p)^4((4q^4)/(3p))^-2

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