Basic Math Examples

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

Step 1

Combine.

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

Step 2

Multiply $y^{2}$ by $y^{\frac{2}{3}}$ by adding the exponents.

Tap for more steps...

Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Combine $2$ and $\frac{3}{3}$ .

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify the numerator.

Tap for more steps...

Step 2.5.1

Multiply $2$ by $3$ .

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

Step 2.5.2

Add $6$ and $2$ .

$\frac{y^{\frac{8}{3}}}{2 \cdot 2^{\frac{2}{3}}}$

Step 3

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

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Raise $2$ to the power of $1$ .

$\frac{y^{\frac{8}{3}}}{2^{1} \cdot 2^{\frac{2}{3}}}$

Step 3.1.2

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

$\frac{y^{\frac{8}{3}}}{2^{1 + \frac{2}{3}}}$

Step 3.2

Write $1$ as a fraction with a common denominator.

$\frac{y^{\frac{8}{3}}}{2^{\frac{3}{3} + \frac{2}{3}}}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{y^{\frac{8}{3}}}{2^{\frac{3 + 2}{3}}}$

Step 3.4

Add $3$ and $2$ .

$\frac{y^{\frac{8}{3}}}{2^{\frac{5}{3}}}$