Evaluate ((b^(3/5))/(b^(1/10)))

$(\frac{b^{\frac{3}{5}}}{b^{\frac{1}{10}}})$

Remove parentheses.

$\frac{b^{\frac{3}{5}}}{b^{\frac{1}{10}}}$

Move $b^{\frac{1}{10}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$b^{\frac{3}{5}} b^{- \frac{1}{10}}$

Multiply $b^{\frac{3}{5}}$ by $b^{- \frac{1}{10}}$ by adding the exponents.

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

$b^{\frac{3}{5} - \frac{1}{10}}$

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

$b^{\frac{3}{5} \cdot \frac{2}{2} - \frac{1}{10}}$

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

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

$b^{\frac{3 \cdot 2}{5 \cdot 2} - \frac{1}{10}}$

Multiply $5$ by $2$ .

$b^{\frac{3 \cdot 2}{10} - \frac{1}{10}}$

Combine the numerators over the common denominator.

$b^{\frac{3 \cdot 2 - 1}{10}}$

Simplify the numerator.

Multiply $3$ by $2$ .

$b^{\frac{6 - 1}{10}}$

Subtract $1$ from $6$ .

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

Cancel the common factor of $5$ and $10$ .

Factor $5$ out of $5$ .

$b^{\frac{5 (1)}{10}}$

Cancel the common factors.

Factor $5$ out of $10$ .

$b^{\frac{5 \cdot 1}{5 \cdot 2}}$

Cancel the common factor.

$b^{\frac{5 \cdot 1}{5 \cdot 2}}$

Rewrite the expression.

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