Simplify 5^(1/4)*5^(4/5)

$5^{\frac{1}{4}} \cdot 5^{\frac{4}{5}}$

Step 1

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

$5^{\frac{1}{4} + \frac{4}{5}}$

Step 2

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$5^{\frac{1}{4} \cdot \frac{5}{5} + \frac{4}{5}}$

Step 3

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$5^{\frac{1}{4} \cdot \frac{5}{5} + \frac{4}{5} \cdot \frac{4}{4}}$

Step 4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{4}$ by $\frac{5}{5}$ .

$5^{\frac{5}{4 \cdot 5} + \frac{4}{5} \cdot \frac{4}{4}}$

Multiply $4$ by $5$ .

$5^{\frac{5}{20} + \frac{4}{5} \cdot \frac{4}{4}}$

Multiply $\frac{4}{5}$ by $\frac{4}{4}$ .

$5^{\frac{5}{20} + \frac{4 \cdot 4}{5 \cdot 4}}$

Multiply $5$ by $4$ .

$5^{\frac{5}{20} + \frac{4 \cdot 4}{20}}$

Step 5

Combine the numerators over the common denominator.

$5^{\frac{5 + 4 \cdot 4}{20}}$

Step 6

Simplify the numerator.

Multiply $4$ by $4$ .

$5^{\frac{5 + 16}{20}}$

Add $5$ and $16$ .

$5^{\frac{21}{20}}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$5^{\frac{21}{20}}$

Decimal Form:

$5.41899193 \dots$