Simplify (3(p^4w^5)^-2)/(3p^7)

$\frac{3 {(p^{4} w^{5})}^{- 2}}{3 p^{7}}$

Step 1

Reduce the expression by cancelling the common factors.

Move ${(p^{4} w^{5})}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{3}{3 p^{7} {(p^{4} w^{5})}^{2}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{3 p^{7} {(p^{4} w^{5})}^{2}}$

Rewrite the expression.

$\frac{1}{p^{7} {(p^{4} w^{5})}^{2}}$

Step 2

Simplify the denominator.

Apply the product rule to $p^{4} w^{5}$ .

$\frac{1}{p^{7} {(p^{4})}^{2} {(w^{5})}^{2}}$

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

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

$\frac{1}{p^{7} p^{4 \cdot 2} {(w^{5})}^{2}}$

Multiply $4$ by $2$ .

$\frac{1}{p^{7} p^{8} {(w^{5})}^{2}}$

Multiply the exponents in ${(w^{5})}^{2}$ .

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

$\frac{1}{p^{7} p^{8} w^{5 \cdot 2}}$

Multiply $5$ by $2$ .

$\frac{1}{p^{7} p^{8} w^{10}}$

Multiply $p^{7}$ by $p^{8}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{p^{7 + 8} w^{10}}$

Add $7$ and $8$ .

$\frac{1}{p^{15} w^{10}}$