Calculus Examples

$x^{\frac{4}{5}} x^{\frac{1}{3}}$

Step 1

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

$x^{\frac{4}{5} + \frac{1}{3}}$

Step 2

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{4}{5}$ by $\frac{3}{3}$ .

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

Step 4.2

Multiply $5$ by $3$ .

$x^{\frac{4 \cdot 3}{15} + \frac{1}{3} \cdot \frac{5}{5}}$

Step 4.3

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$x^{\frac{4 \cdot 3}{15} + \frac{5}{3 \cdot 5}}$

Step 4.4

Multiply $3$ by $5$ .

$x^{\frac{4 \cdot 3}{15} + \frac{5}{15}}$

Step 5

Combine the numerators over the common denominator.

$x^{\frac{4 \cdot 3 + 5}{15}}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $4$ by $3$ .

$x^{\frac{12 + 5}{15}}$

Step 6.2

Add $12$ and $5$ .

$x^{\frac{17}{15}}$