Simplify ((s^-4)/(t^-1))^-2

${(\frac{s^{- 4}}{t^{- 1}})}^{- 2}$

Step 1

Move $s^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{1}{t^{- 1} s^{4}})}^{- 2}$

Step 2

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

${(\frac{t}{s^{4}})}^{- 2}$

Step 3

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

${(\frac{s^{4}}{t})}^{2}$

Step 4

Apply the product rule to $\frac{s^{4}}{t}$ .

$\frac{{(s^{4})}^{2}}{t^{2}}$

Step 5

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

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

$\frac{s^{4 \cdot 2}}{t^{2}}$

Multiply $4$ by $2$ .

$\frac{s^{8}}{t^{2}}$