Algebra Examples

${(m^{3})}^{- 1} {(x^{2})}^{5}$

Step 1

Multiply the exponents in ${(m^{3})}^{- 1}$ .

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Step 1.1

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

$m^{3 \cdot - 1} {(x^{2})}^{5}$

Step 1.2

Multiply $3$ by $- 1$ .

$m^{- 3} {(x^{2})}^{5}$

Step 2

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

$\frac{1}{m^{3}} {(x^{2})}^{5}$

Step 3

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

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Step 3.1

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

$\frac{1}{m^{3}} x^{2 \cdot 5}$

Step 3.2

Multiply $2$ by $5$ .

$\frac{1}{m^{3}} x^{10}$

Step 4

Combine $\frac{1}{m^{3}}$ and $x^{10}$ .

$\frac{x^{10}}{m^{3}}$