Simplify y^(2/5)*y^(3/8)

$y^{\frac{2}{5}} \cdot y^{\frac{3}{8}}$

Step 1

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

$y^{\frac{2}{5} + \frac{3}{8}}$

Step 2

To write $\frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$y^{\frac{2}{5} \cdot \frac{8}{8} + \frac{3}{8}}$

Step 3

To write $\frac{3}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y^{\frac{2}{5} \cdot \frac{8}{8} + \frac{3}{8} \cdot \frac{5}{5}}$

Step 4

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{5}$ by $\frac{8}{8}$ .

$y^{\frac{2 \cdot 8}{5 \cdot 8} + \frac{3}{8} \cdot \frac{5}{5}}$

Multiply $5$ by $8$ .

$y^{\frac{2 \cdot 8}{40} + \frac{3}{8} \cdot \frac{5}{5}}$

Multiply $\frac{3}{8}$ by $\frac{5}{5}$ .

$y^{\frac{2 \cdot 8}{40} + \frac{3 \cdot 5}{8 \cdot 5}}$

Multiply $8$ by $5$ .

$y^{\frac{2 \cdot 8}{40} + \frac{3 \cdot 5}{40}}$

Step 5

Combine the numerators over the common denominator.

$y^{\frac{2 \cdot 8 + 3 \cdot 5}{40}}$

Step 6

Simplify the numerator.

Multiply $2$ by $8$ .

$y^{\frac{16 + 3 \cdot 5}{40}}$

Multiply $3$ by $5$ .

$y^{\frac{16 + 15}{40}}$

Add $16$ and $15$ .

$y^{\frac{31}{40}}$