Algebra Examples

${(\frac{8 a b^{- 3}}{b^{5}})}^{2}$

Step 1

Move $b^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{8 a}{b^{5} b^{3}})}^{2}$

Step 2

Multiply $b^{5}$ by $b^{3}$ by adding the exponents.

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Step 2.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{8 a}{b^{5 + 3}})}^{2}$

Step 2.2

Add $5$ and $3$ .

${(\frac{8 a}{b^{8}})}^{2}$

Step 3

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

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Step 3.1

Apply the product rule to $\frac{8 a}{b^{8}}$ .

$\frac{{(8 a)}^{2}}{{(b^{8})}^{2}}$

Step 3.2

Apply the product rule to $8 a$ .

$\frac{8^{2} a^{2}}{{(b^{8})}^{2}}$

Step 4

Raise $8$ to the power of $2$ .

$\frac{64 a^{2}}{{(b^{8})}^{2}}$

Step 5

Multiply the exponents in ${(b^{8})}^{2}$ .

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Step 5.1

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

$\frac{64 a^{2}}{b^{8 \cdot 2}}$

Step 5.2

Multiply $8$ by $2$ .

$\frac{64 a^{2}}{b^{16}}$