Algebra Examples

$(c y^{3}) (9 y^{d}) = 18 y^{6}$

Step 1

Simplify.

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Step 1.1

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

$c (9 y^{3 + d}) = 18 y^{6}$

Step 1.2

Remove parentheses.

$c \cdot 9 y^{3 + d} = 18 y^{6}$

Step 2

Divide each term in $c \cdot (9 y^{3 + d}) = 18 y^{6}$ by $9 y^{3 + d}$ and simplify.

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Step 2.1

Divide each term in $c \cdot (9 y^{3 + d}) = 18 y^{6}$ by $9 y^{3 + d}$ .

$\frac{c \cdot (9 y^{3 + d})}{9 y^{3 + d}} = \frac{18 y^{6}}{9 y^{3 + d}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $9$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{c \cdot (9 y^{3 + d})}{9 y^{3 + d}} = \frac{18 y^{6}}{9 y^{3 + d}}$

Step 2.2.1.2

Rewrite the expression.

$\frac{c \cdot (y^{3 + d})}{y^{3 + d}} = \frac{18 y^{6}}{9 y^{3 + d}}$

Step 2.2.2

Cancel the common factor of $y^{3 + d}$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{c \cdot y^{3 + d}}{y^{3 + d}} = \frac{18 y^{6}}{9 y^{3 + d}}$

Step 2.2.2.2

Divide $c$ by $1$ .

$c = \frac{18 y^{6}}{9 y^{3 + d}}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Reduce the expression by cancelling the common factors.

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Step 2.3.1.1

Cancel the common factor of $18$ and $9$ .

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Step 2.3.1.1.1

Factor $9$ out of $18 y^{6}$ .

$c = \frac{9 (2 y^{6})}{9 y^{3 + d}}$

Step 2.3.1.1.2

Cancel the common factors.

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Step 2.3.1.1.2.1

Factor $9$ out of $9 y^{3 + d}$ .

$c = \frac{9 (2 y^{6})}{9 (y^{3 + d})}$

Step 2.3.1.1.2.2

Cancel the common factor.

$c = \frac{9 (2 y^{6})}{9 y^{3 + d}}$

Step 2.3.1.1.2.3

Rewrite the expression.

$c = \frac{2 y^{6}}{y^{3 + d}}$

Step 2.3.1.2

Cancel the common factor of $y^{6}$ and $y^{3 + d}$ .

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Step 2.3.1.2.1

Factor $y^{3 + d}$ out of $2 y^{6}$ .

$c = \frac{y^{3 + d} (2 y^{6 - (3 + d)})}{y^{3 + d}}$

Step 2.3.1.2.2

Cancel the common factors.

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Step 2.3.1.2.2.1

Multiply by $1$ .

$c = \frac{y^{3 + d} (2 y^{6 - (3 + d)})}{y^{3 + d} \cdot 1}$

Step 2.3.1.2.2.2

Cancel the common factor.

$c = \frac{y^{3 + d} (2 y^{6 - (3 + d)})}{y^{3 + d} \cdot 1}$

Step 2.3.1.2.2.3

Rewrite the expression.

$c = \frac{2 y^{6 - (3 + d)}}{1}$

Step 2.3.1.2.2.4

Divide $2 y^{6 - (3 + d)}$ by $1$ .

$c = 2 y^{6 - (3 + d)}$

Step 2.3.2

Simplify each term.

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Step 2.3.2.1

Apply the distributive property.

$c = 2 y^{6 - 1 \cdot 3 - d}$

Step 2.3.2.2

Multiply $- 1$ by $3$ .

$c = 2 y^{6 - 3 - d}$

Step 2.3.3

Subtract $3$ from $6$ .

$c = 2 y^{3 - d}$