Algebra Examples

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

Step 1

Simplify the expression.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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

Step 3

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

$\frac{2}{3} \cdot 27$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Factor $3$ out of $27$ .

$\frac{2}{3} \cdot (3 (9))$

Step 4.2

Cancel the common factor.

$\frac{2}{3} \cdot (3 \cdot 9)$

Step 4.3

Rewrite the expression.

$2 \cdot 9$

Step 5

Multiply $2$ by $9$ .

$18$