Simplify (x^(4/13))(x^(5/26))

$(x^{\frac{4}{13}}) (x^{\frac{5}{26}})$

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

$x^{\frac{4}{13} + \frac{5}{26}}$

To write $\frac{4}{13}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x^{\frac{4}{13} \cdot \frac{2}{2} + \frac{5}{26}}$

Write each expression with a common denominator of $26$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{13}$ by $\frac{2}{2}$ .

$x^{\frac{4 \cdot 2}{13 \cdot 2} + \frac{5}{26}}$

Multiply $13$ by $2$ .

$x^{\frac{4 \cdot 2}{26} + \frac{5}{26}}$

Combine the numerators over the common denominator.

$x^{\frac{4 \cdot 2 + 5}{26}}$

Simplify the numerator.

Multiply $4$ by $2$ .

$x^{\frac{8 + 5}{26}}$

Add $8$ and $5$ .

$x^{\frac{13}{26}}$

Cancel the common factor of $13$ and $26$ .

Factor $13$ out of $13$ .

$x^{\frac{13 (1)}{26}}$

Cancel the common factors.

Factor $13$ out of $26$ .

$x^{\frac{13 \cdot 1}{13 \cdot 2}}$

Cancel the common factor.

$x^{\frac{13 \cdot 1}{13 \cdot 2}}$

Rewrite the expression.

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