Algebra Examples

$\frac{9^{\frac{2}{3}} \cdot 3^{\frac{5}{3}}}{6^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $9$ as $3^{2}$ .

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

Step 1.2

Multiply the exponents in ${(3^{2})}^{\frac{2}{3}}$ .

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Step 1.2.1

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

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

Step 1.2.2

Multiply $2 (\frac{2}{3})$ .

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Step 1.2.2.1

Combine $2$ and $\frac{2}{3}$ .

$\frac{3^{\frac{2 \cdot 2}{3}} \cdot 3^{\frac{5}{3}}}{6^{2}}$

Step 1.2.2.2

Multiply $2$ by $2$ .

$\frac{3^{\frac{4}{3}} \cdot 3^{\frac{5}{3}}}{6^{2}}$

Step 1.3

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

$\frac{3^{\frac{4}{3} + \frac{5}{3}}}{6^{2}}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{3^{\frac{4 + 5}{3}}}{6^{2}}$

Step 1.5

Add $4$ and $5$ .

$\frac{3^{\frac{9}{3}}}{6^{2}}$

Step 1.6

Cancel the common factor of $9$ and $3$ .

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Step 1.6.1

Factor $3$ out of $9$ .

$\frac{3^{\frac{3 \cdot 3}{3}}}{6^{2}}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $3$ out of $3$ .

$\frac{3^{\frac{3 \cdot 3}{3 (1)}}}{6^{2}}$

Step 1.6.2.2

Cancel the common factor.

$\frac{3^{\frac{3 \cdot 3}{3 \cdot 1}}}{6^{2}}$

Step 1.6.2.3

Rewrite the expression.

$\frac{3^{\frac{3}{1}}}{6^{2}}$

Step 1.6.2.4

Divide $3$ by $1$ .

$\frac{3^{3}}{6^{2}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Raise $6$ to the power of $2$ .

$\frac{3^{3}}{36}$

Step 2.2

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

$\frac{27}{36}$

Step 2.3

Cancel the common factor of $27$ and $36$ .

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Step 2.3.1

Factor $9$ out of $27$ .

$\frac{9 (3)}{36}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $9$ out of $36$ .

$\frac{9 \cdot 3}{9 \cdot 4}$

Step 2.3.2.2

Cancel the common factor.

$\frac{9 \cdot 3}{9 \cdot 4}$

Step 2.3.2.3

Rewrite the expression.

$\frac{3}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{4}$

Decimal Form:

$0.75$