Algebra Examples

${(a^{4})}^{6} {(b^{5})}^{- 2}$

Step 1

Multiply the exponents in ${(a^{4})}^{6}$ .

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Step 1.1

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

$a^{4 \cdot 6} {(b^{5})}^{- 2}$

Step 1.2

Multiply $4$ by $6$ .

$a^{24} {(b^{5})}^{- 2}$

Step 2

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

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Step 2.1

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

$a^{24} b^{5 \cdot - 2}$

Step 2.2

Multiply $5$ by $- 2$ .

$a^{24} b^{- 10}$

Step 3

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

$a^{24} \frac{1}{b^{10}}$

Step 4

Combine $a^{24}$ and $\frac{1}{b^{10}}$ .

$\frac{a^{24}}{b^{10}}$