Simplify (5^(2/7))(5^(5/6))

$(5^{\frac{2}{7}}) (5^{\frac{5}{6}})$

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

$5^{\frac{2}{7} + \frac{5}{6}}$

To write $\frac{2}{7}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$5^{\frac{2}{7} \cdot \frac{6}{6} + \frac{5}{6}}$

To write $\frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$5^{\frac{2}{7} \cdot \frac{6}{6} + \frac{5}{6} \cdot \frac{7}{7}}$

Write each expression with a common denominator of $42$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{7}$ by $\frac{6}{6}$ .

$5^{\frac{2 \cdot 6}{7 \cdot 6} + \frac{5}{6} \cdot \frac{7}{7}}$

Multiply $7$ by $6$ .

$5^{\frac{2 \cdot 6}{42} + \frac{5}{6} \cdot \frac{7}{7}}$

Multiply $\frac{5}{6}$ by $\frac{7}{7}$ .

$5^{\frac{2 \cdot 6}{42} + \frac{5 \cdot 7}{6 \cdot 7}}$

Multiply $6$ by $7$ .

$5^{\frac{2 \cdot 6}{42} + \frac{5 \cdot 7}{42}}$

Combine the numerators over the common denominator.

$5^{\frac{2 \cdot 6 + 5 \cdot 7}{42}}$

Simplify the numerator.

Multiply $2$ by $6$ .

$5^{\frac{12 + 5 \cdot 7}{42}}$

Multiply $5$ by $7$ .

$5^{\frac{12 + 35}{42}}$

Add $12$ and $35$ .

$5^{\frac{47}{42}}$

The result can be shown in multiple forms.

Exact Form:

$5^{\frac{47}{42}}$

Decimal Form:

$6.05592822 \dots$