Algebra Examples

$\frac{30^{\frac{5}{9}} \cdot 30^{\frac{2}{3}}}{2^{\frac{11}{9}}}$

Step 1

Multiply $30^{\frac{5}{9}}$ by $30^{\frac{2}{3}}$ by adding the exponents.

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Step 1.1

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

$\frac{30^{\frac{5}{9} + \frac{2}{3}}}{2^{\frac{11}{9}}}$

Step 1.2

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{30^{\frac{5}{9} + \frac{2}{3} \cdot \frac{3}{3}}}{2^{\frac{11}{9}}}$

Step 1.3

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{2}{3}$ by $\frac{3}{3}$ .

$\frac{30^{\frac{5}{9} + \frac{2 \cdot 3}{3 \cdot 3}}}{2^{\frac{11}{9}}}$

Step 1.3.2

Multiply $3$ by $3$ .

$\frac{30^{\frac{5}{9} + \frac{2 \cdot 3}{9}}}{2^{\frac{11}{9}}}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{30^{\frac{5 + 2 \cdot 3}{9}}}{2^{\frac{11}{9}}}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $2$ by $3$ .

$\frac{30^{\frac{5 + 6}{9}}}{2^{\frac{11}{9}}}$

Step 1.5.2

Add $5$ and $6$ .

$\frac{30^{\frac{11}{9}}}{2^{\frac{11}{9}}}$

Step 2

Use the power of quotient rule $\frac{a^{m}}{b^{m}} = {(\frac{a}{b})}^{m}$ .

${(\frac{30}{2})}^{\frac{11}{9}}$

Step 3

Divide $30$ by $2$ .

$15^{\frac{11}{9}}$