Algebra Examples

$y^{\frac{1}{2}} (y^{\frac{1}{2}} - y^{\frac{2}{3}})$

Step 1

Apply the distributive property.

$y^{\frac{1}{2}} y^{\frac{1}{2}} + y^{\frac{1}{2}} (- y^{\frac{2}{3}})$

Step 2

Multiply $y^{\frac{1}{2}}$ by $y^{\frac{1}{2}}$ by adding the exponents.

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Step 2.1

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

$y^{\frac{1}{2} + \frac{1}{2}} + y^{\frac{1}{2}} (- y^{\frac{2}{3}})$

Step 2.2

Combine the numerators over the common denominator.

$y^{\frac{1 + 1}{2}} + y^{\frac{1}{2}} (- y^{\frac{2}{3}})$

Step 2.3

Add $1$ and $1$ .

$y^{\frac{2}{2}} + y^{\frac{1}{2}} (- y^{\frac{2}{3}})$

Step 2.4

Divide $2$ by $2$ .

$y^{1} + y^{\frac{1}{2}} (- y^{\frac{2}{3}})$

Step 3

Simplify $y^{1}$ .

$y + y^{\frac{1}{2}} (- y^{\frac{2}{3}})$

Step 4

Rewrite using the commutative property of multiplication.

$y - y^{\frac{1}{2}} y^{\frac{2}{3}}$

Step 5

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

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Step 5.1

Move $y^{\frac{2}{3}}$ .

$y - (y^{\frac{2}{3}} y^{\frac{1}{2}})$

Step 5.2

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

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

Step 5.3

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

$y - y^{\frac{2}{3} \cdot \frac{2}{2} + \frac{1}{2}}$

Step 5.4

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y - y^{\frac{2}{3} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{3}{3}}$

Step 5.5

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

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Step 5.5.1

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

$y - y^{\frac{2 \cdot 2}{3 \cdot 2} + \frac{1}{2} \cdot \frac{3}{3}}$

Step 5.5.2

Multiply $3$ by $2$ .

$y - y^{\frac{2 \cdot 2}{6} + \frac{1}{2} \cdot \frac{3}{3}}$

Step 5.5.3

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

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

Step 5.5.4

Multiply $2$ by $3$ .

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

Step 5.6

Combine the numerators over the common denominator.

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

Step 5.7

Simplify the numerator.

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Step 5.7.1

Multiply $2$ by $2$ .

$y - y^{\frac{4 + 3}{6}}$

Step 5.7.2

Add $4$ and $3$ .

$y - y^{\frac{7}{6}}$