Simplify x^(2/9)*x^(5/18)

$x^{\frac{2}{9}} \cdot x^{\frac{5}{18}}$

Step 1

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

$x^{\frac{2}{9} + \frac{5}{18}}$

Step 2

To write $\frac{2}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x^{\frac{2}{9} \cdot \frac{2}{2} + \frac{5}{18}}$

Step 3

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{9}$ by $\frac{2}{2}$ .

$x^{\frac{2 \cdot 2}{9 \cdot 2} + \frac{5}{18}}$

Multiply $9$ by $2$ .

$x^{\frac{2 \cdot 2}{18} + \frac{5}{18}}$

Step 4

Combine the numerators over the common denominator.

$x^{\frac{2 \cdot 2 + 5}{18}}$

Step 5

Simplify the numerator.

Multiply $2$ by $2$ .

$x^{\frac{4 + 5}{18}}$

Add $4$ and $5$ .

$x^{\frac{9}{18}}$

Step 6

Cancel the common factor of $9$ and $18$ .

Factor $9$ out of $9$ .

$x^{\frac{9 (1)}{18}}$

Cancel the common factors.

Factor $9$ out of $18$ .

$x^{\frac{9 \cdot 1}{9 \cdot 2}}$

Cancel the common factor.

$x^{\frac{9 \cdot 1}{9 \cdot 2}}$

Rewrite the expression.

$x^{\frac{1}{2}}$