Simplify (t^(2/3))/(5t^(1/2)*t^(-3/4))

$\frac{t^{\frac{2}{3}}}{5 t^{\frac{1}{2}} \cdot t^{- \frac{3}{4}}}$

Multiply $t^{\frac{1}{2}}$ by $t^{- \frac{3}{4}}$ by adding the exponents.

Move $t^{- \frac{3}{4}}$ .

$\frac{t^{\frac{2}{3}}}{5 (t^{- \frac{3}{4}} t^{\frac{1}{2}})}$

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

$\frac{t^{\frac{2}{3}}}{5 t^{- \frac{3}{4} + \frac{1}{2}}}$

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{t^{\frac{2}{3}}}{5 t^{- \frac{3}{4} + \frac{1}{2} \cdot \frac{2}{2}}}$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$\frac{t^{\frac{2}{3}}}{5 t^{- \frac{3}{4} + \frac{2}{2 \cdot 2}}}$

Multiply $2$ by $2$ .

$\frac{t^{\frac{2}{3}}}{5 t^{- \frac{3}{4} + \frac{2}{4}}}$

Combine the numerators over the common denominator.

$\frac{t^{\frac{2}{3}}}{5 t^{\frac{- 3 + 2}{4}}}$

Add $- 3$ and $2$ .

$\frac{t^{\frac{2}{3}}}{5 t^{\frac{- 1}{4}}}$

Move the negative in front of the fraction.

$\frac{t^{\frac{2}{3}}}{5 t^{- \frac{1}{4}}}$

Move $t^{- \frac{1}{4}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{t^{\frac{2}{3}} t^{\frac{1}{4}}}{5}$

Multiply $t^{\frac{2}{3}}$ by $t^{\frac{1}{4}}$ by adding the exponents.

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

$\frac{t^{\frac{2}{3} + \frac{1}{4}}}{5}$

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{t^{\frac{2}{3} \cdot \frac{4}{4} + \frac{1}{4}}}{5}$

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{t^{\frac{2}{3} \cdot \frac{4}{4} + \frac{1}{4} \cdot \frac{3}{3}}}{5}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{3}$ by $\frac{4}{4}$ .

$\frac{t^{\frac{2 \cdot 4}{3 \cdot 4} + \frac{1}{4} \cdot \frac{3}{3}}}{5}$

Multiply $3$ by $4$ .

$\frac{t^{\frac{2 \cdot 4}{12} + \frac{1}{4} \cdot \frac{3}{3}}}{5}$

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$\frac{t^{\frac{2 \cdot 4}{12} + \frac{3}{4 \cdot 3}}}{5}$

Multiply $4$ by $3$ .

$\frac{t^{\frac{2 \cdot 4}{12} + \frac{3}{12}}}{5}$

Combine the numerators over the common denominator.

$\frac{t^{\frac{2 \cdot 4 + 3}{12}}}{5}$

Simplify the numerator.

Multiply $2$ by $4$ .

$\frac{t^{\frac{8 + 3}{12}}}{5}$

Add $8$ and $3$ .

$\frac{t^{\frac{11}{12}}}{5}$