Basic Math Examples

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

Step 1

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

$\frac{1}{{(4 a^{2} b^{5})}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $4 a^{2} b^{5}$ .

$\frac{1}{{(4 a^{2})}^{2} {(b^{5})}^{2}}$

Step 2.2

Apply the product rule to $4 a^{2}$ .

$\frac{1}{4^{2} {(a^{2})}^{2} {(b^{5})}^{2}}$

Step 2.3

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

$\frac{1}{16 {(a^{2})}^{2} {(b^{5})}^{2}}$

Step 2.4

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

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Step 2.4.1

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

$\frac{1}{16 a^{2 \cdot 2} {(b^{5})}^{2}}$

Step 2.4.2

Multiply $2$ by $2$ .

$\frac{1}{16 a^{4} {(b^{5})}^{2}}$

Step 2.5

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

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Step 2.5.1

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

$\frac{1}{16 a^{4} b^{5 \cdot 2}}$

Step 2.5.2

Multiply $5$ by $2$ .

$\frac{1}{16 a^{4} b^{10}}$