Algebra Examples

${(4^{- 1} s^{3})}^{- 2}$

Step 1

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

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

Step 2

Combine $\frac{1}{4}$ and $s^{3}$ .

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

Step 3

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

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

Step 4

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

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

Step 5

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

$\frac{16}{{(s^{3})}^{2}}$

Step 6

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

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Step 6.1

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

$\frac{16}{s^{3 \cdot 2}}$

Step 6.2

Multiply $3$ by $2$ .

$\frac{16}{s^{6}}$