Calculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

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

Step 4.2

Multiply $2$ by $3$ .

$y^{\frac{5 \cdot 3}{6} + \frac{2}{3} \cdot \frac{2}{2}}$

Step 4.3

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

$y^{\frac{5 \cdot 3}{6} + \frac{2 \cdot 2}{3 \cdot 2}}$

Step 4.4

Multiply $3$ by $2$ .

$y^{\frac{5 \cdot 3}{6} + \frac{2 \cdot 2}{6}}$

Step 5

Combine the numerators over the common denominator.

$y^{\frac{5 \cdot 3 + 2 \cdot 2}{6}}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $5$ by $3$ .

$y^{\frac{15 + 2 \cdot 2}{6}}$

Step 6.2

Multiply $2$ by $2$ .

$y^{\frac{15 + 4}{6}}$

Step 6.3

Add $15$ and $4$ .

$y^{\frac{19}{6}}$