Evaluate 5^(3/5)*5^(7/10)

$5^{\frac{3}{5}} \cdot 5^{\frac{7}{10}}$

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

$5^{\frac{3}{5} + \frac{7}{10}}$

To write $\frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$5^{\frac{3}{5} \cdot \frac{2}{2} + \frac{7}{10}}$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{3}{5}$ and $\frac{2}{2}$ .

$5^{\frac{3 \cdot 2}{5 \cdot 2} + \frac{7}{10}}$

Multiply $5$ by $2$ .

$5^{\frac{3 \cdot 2}{10} + \frac{7}{10}}$

Combine the numerators over the common denominator.

$5^{\frac{3 \cdot 2 + 7}{10}}$

Simplify the numerator.

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Multiply $3$ by $2$ .

$5^{\frac{6 + 7}{10}}$

Add $6$ and $7$ .

$5^{\frac{13}{10}}$

The result can be shown in multiple forms.

Exact Form:

$5^{\frac{13}{10}}$

Decimal Form:

$8.10328298 \dots$

Evaluate 5^(3/5)*5^(7/10)

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