Algebra Examples

${(3 a^{3} b^{- 1} a)}^{2}$

Step 1

Multiply $a^{3}$ by $a$ by adding the exponents.

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Step 1.1

Move $a$ .

${(3 (a \cdot a^{3}) b^{- 1})}^{2}$

Step 1.2

Multiply $a$ by $a^{3}$ .

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Step 1.2.1

Raise $a$ to the power of $1$ .

${(3 (a^{1} a^{3}) b^{- 1})}^{2}$

Step 1.2.2

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

${(3 a^{1 + 3} b^{- 1})}^{2}$

Step 1.3

Add $1$ and $3$ .

${(3 a^{4} b^{- 1})}^{2}$

Step 2

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

${(3 a^{4} \frac{1}{b})}^{2}$

Step 3

Multiply $3 a^{4} \frac{1}{b}$ .

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Step 3.1

Combine $3$ and $\frac{1}{b}$ .

${(a^{4} \frac{3}{b})}^{2}$

Step 3.2

Combine $a^{4}$ and $\frac{3}{b}$ .

${(\frac{a^{4} \cdot 3}{b})}^{2}$

Step 4

Move $3$ to the left of $a^{4}$ .

${(\frac{3 \cdot a^{4}}{b})}^{2}$

Step 5

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

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Step 5.1

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

$\frac{{(3 a^{4})}^{2}}{b^{2}}$

Step 5.2

Apply the product rule to $3 a^{4}$ .

$\frac{3^{2} {(a^{4})}^{2}}{b^{2}}$

Step 6

Simplify the numerator.

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Step 6.1

Raise $3$ to the power of $2$ .

$\frac{9 {(a^{4})}^{2}}{b^{2}}$

Step 6.2

Multiply the exponents in ${(a^{4})}^{2}$ .

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Step 6.2.1

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

$\frac{9 a^{4 \cdot 2}}{b^{2}}$

Step 6.2.2

Multiply $4$ by $2$ .

$\frac{9 a^{8}}{b^{2}}$