Simplify ((q^-1r^3)/(qr^-2))^-5

${(\frac{q^{- 1} r^{3}}{q r^{- 2}})}^{- 5}$

Step 1

Move $q^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{r^{3}}{q r^{- 2} q})}^{- 5}$

Step 2

Multiply $q$ by $q$ by adding the exponents.

Move $q$ .

${(\frac{r^{3}}{q \cdot q r^{- 2}})}^{- 5}$

Multiply $q$ by $q$ .

${(\frac{r^{3}}{q^{2} r^{- 2}})}^{- 5}$

Step 3

Move $r^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{r^{3} r^{2}}{q^{2}})}^{- 5}$

Step 4

Multiply $r^{3}$ by $r^{2}$ by adding the exponents.

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

${(\frac{r^{3 + 2}}{q^{2}})}^{- 5}$

Add $3$ and $2$ .

${(\frac{r^{5}}{q^{2}})}^{- 5}$

Step 5

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

${(\frac{q^{2}}{r^{5}})}^{5}$

Step 6

Apply the product rule to $\frac{q^{2}}{r^{5}}$ .

$\frac{{(q^{2})}^{5}}{{(r^{5})}^{5}}$

Step 7

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

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

$\frac{q^{2 \cdot 5}}{{(r^{5})}^{5}}$

Multiply $2$ by $5$ .

$\frac{q^{10}}{{(r^{5})}^{5}}$

Step 8

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

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

$\frac{q^{10}}{r^{5 \cdot 5}}$

Multiply $5$ by $5$ .

$\frac{q^{10}}{r^{25}}$