Basic Math Examples

$\frac{x^{\frac{3}{4}} x^{\frac{1}{2}}}{x^{\frac{1}{4}}}$

Step 1

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

Tap for more steps...

Step 1.1

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

$\frac{x^{\frac{3}{4} + \frac{1}{2}}}{x^{\frac{1}{4}}}$

Step 1.2

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

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

Step 1.3

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

Tap for more steps...

Step 1.3.1

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

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

Step 1.3.2

Multiply $2$ by $2$ .

$\frac{x^{\frac{3}{4} + \frac{2}{4}}}{x^{\frac{1}{4}}}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x^{\frac{3 + 2}{4}}}{x^{\frac{1}{4}}}$

Step 1.5

Add $3$ and $2$ .

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

Step 2

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

$x^{\frac{5}{4}} x^{- \frac{1}{4}}$

Step 3

Multiply $x^{\frac{5}{4}}$ by $x^{- \frac{1}{4}}$ by adding the exponents.

Tap for more steps...

Step 3.1

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

$x^{\frac{5}{4} - \frac{1}{4}}$

Step 3.2

Combine the numerators over the common denominator.

$x^{\frac{5 - 1}{4}}$

Step 3.3

Subtract $1$ from $5$ .

$x^{\frac{4}{4}}$

Step 3.4

Divide $4$ by $4$ .

$x^{1}$

Step 4

Simplify $x^{1}$ .

$x$