Algebra Examples

$y^{\frac{5}{9}} (y^{\frac{2}{9}} - 4 y^{\frac{3}{9}})$

Step 1

Cancel the common factor of $3$ and $9$ .

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Step 1.1

Factor $3$ out of $3$ .

$y^{\frac{5}{9}} (y^{\frac{2}{9}} - 4 y^{\frac{3 (1)}{9}})$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $9$ .

$y^{\frac{5}{9}} (y^{\frac{2}{9}} - 4 y^{\frac{3 \cdot 1}{3 \cdot 3}})$

Step 1.2.2

Cancel the common factor.

$y^{\frac{5}{9}} (y^{\frac{2}{9}} - 4 y^{\frac{3 \cdot 1}{3 \cdot 3}})$

Step 1.2.3

Rewrite the expression.

$y^{\frac{5}{9}} (y^{\frac{2}{9}} - 4 y^{\frac{1}{3}})$

Step 2

Apply the distributive property.

$y^{\frac{5}{9}} y^{\frac{2}{9}} + y^{\frac{5}{9}} (- 4 y^{\frac{1}{3}})$

Step 3

Multiply $y^{\frac{5}{9}}$ by $y^{\frac{2}{9}}$ by adding the exponents.

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Step 3.1

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

$y^{\frac{5}{9} + \frac{2}{9}} + y^{\frac{5}{9}} (- 4 y^{\frac{1}{3}})$

Step 3.2

Combine the numerators over the common denominator.

$y^{\frac{5 + 2}{9}} + y^{\frac{5}{9}} (- 4 y^{\frac{1}{3}})$

Step 3.3

Add $5$ and $2$ .

$y^{\frac{7}{9}} + y^{\frac{5}{9}} (- 4 y^{\frac{1}{3}})$

Step 4

Rewrite using the commutative property of multiplication.

$y^{\frac{7}{9}} - 4 y^{\frac{5}{9}} y^{\frac{1}{3}}$

Step 5

Multiply $y^{\frac{5}{9}}$ by $y^{\frac{1}{3}}$ by adding the exponents.

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Step 5.1

Move $y^{\frac{1}{3}}$ .

$y^{\frac{7}{9}} - 4 (y^{\frac{1}{3}} y^{\frac{5}{9}})$

Step 5.2

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

$y^{\frac{7}{9}} - 4 y^{\frac{1}{3} + \frac{5}{9}}$

Step 5.3

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

$y^{\frac{7}{9}} - 4 y^{\frac{1}{3} \cdot \frac{3}{3} + \frac{5}{9}}$

Step 5.4

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.4.1

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

$y^{\frac{7}{9}} - 4 y^{\frac{3}{3 \cdot 3} + \frac{5}{9}}$

Step 5.4.2

Multiply $3$ by $3$ .

$y^{\frac{7}{9}} - 4 y^{\frac{3}{9} + \frac{5}{9}}$

Step 5.5

Combine the numerators over the common denominator.

$y^{\frac{7}{9}} - 4 y^{\frac{3 + 5}{9}}$

Step 5.6

Add $3$ and $5$ .

$y^{\frac{7}{9}} - 4 y^{\frac{8}{9}}$