Pre-Algebra Examples

${(\frac{3}{5} \cdot (a^{6} b^{9}))}^{2}$

Step 1

Multiply $\frac{3}{5} (a^{6} b^{9})$ .

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Step 1.1

Combine $a^{6}$ and $\frac{3}{5}$ .

${(\frac{a^{6} \cdot 3}{5} b^{9})}^{2}$

Step 1.2

Combine $\frac{a^{6} \cdot 3}{5}$ and $b^{9}$ .

${(\frac{a^{6} \cdot 3 b^{9}}{5})}^{2}$

Step 2

Move $3$ to the left of $a^{6}$ .

${(\frac{3 \cdot a^{6} b^{9}}{5})}^{2}$

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 $\frac{3 a^{6} b^{9}}{5}$ .

$\frac{{(3 a^{6} b^{9})}^{2}}{5^{2}}$

Step 3.2

Apply the product rule to $3 a^{6} b^{9}$ .

$\frac{{(3 a^{6})}^{2} {(b^{9})}^{2}}{5^{2}}$

Step 3.3

Apply the product rule to $3 a^{6}$ .

$\frac{3^{2} {(a^{6})}^{2} {(b^{9})}^{2}}{5^{2}}$

Step 4

Simplify the numerator.

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Step 4.1

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

$\frac{9 {(a^{6})}^{2} {(b^{9})}^{2}}{5^{2}}$

Step 4.2

Multiply the exponents in ${(a^{6})}^{2}$ .

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Step 4.2.1

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

$\frac{9 a^{6 \cdot 2} {(b^{9})}^{2}}{5^{2}}$

Step 4.2.2

Multiply $6$ by $2$ .

$\frac{9 a^{12} {(b^{9})}^{2}}{5^{2}}$

Step 4.3

Multiply the exponents in ${(b^{9})}^{2}$ .

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Step 4.3.1

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

$\frac{9 a^{12} b^{9 \cdot 2}}{5^{2}}$

Step 4.3.2

Multiply $9$ by $2$ .

$\frac{9 a^{12} b^{18}}{5^{2}}$

Step 5

Raise $5$ to the power of $2$ .

$\frac{9 a^{12} b^{18}}{25}$