Simplify (5s^-2t^4)^-3

${(5 s^{- 2} t^{4})}^{- 3}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(5 \frac{1}{s^{2}} t^{4})}^{- 3}$

Step 2

Combine $5$ and $\frac{1}{s^{2}}$ .

${(\frac{5}{s^{2}} t^{4})}^{- 3}$

Step 3

Combine $\frac{5}{s^{2}}$ and $t^{4}$ .

${(\frac{5 t^{4}}{s^{2}})}^{- 3}$

Step 4

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

${(\frac{s^{2}}{5 t^{4}})}^{3}$

Step 5

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

Apply the product rule to $\frac{s^{2}}{5 t^{4}}$ .

$\frac{{(s^{2})}^{3}}{{(5 t^{4})}^{3}}$

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

$\frac{{(s^{2})}^{3}}{5^{3} {(t^{4})}^{3}}$

Step 6

Multiply the exponents in ${(s^{2})}^{3}$ .

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

$\frac{s^{2 \cdot 3}}{5^{3} {(t^{4})}^{3}}$

Multiply $2$ by $3$ .

$\frac{s^{6}}{5^{3} {(t^{4})}^{3}}$

Step 7

Simplify the denominator.

Raise $5$ to the power of $3$ .

$\frac{s^{6}}{125 {(t^{4})}^{3}}$

Multiply the exponents in ${(t^{4})}^{3}$ .

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

$\frac{s^{6}}{125 t^{4 \cdot 3}}$

Multiply $4$ by $3$ .

$\frac{s^{6}}{125 t^{12}}$