Algebra Examples

$\frac{{(- 3 x^{6})}^{2}}{5 x^{3} \cdot 3 x^{3}}$

Step 1

Multiply $x^{3}$ by $x^{3}$ by adding the exponents.

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Step 1.1

Move $x^{3}$ .

$\frac{{(- 3 x^{6})}^{2}}{5 (x^{3} x^{3}) \cdot 3}$

Step 1.2

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

$\frac{{(- 3 x^{6})}^{2}}{5 x^{3 + 3} \cdot 3}$

Step 1.3

Add $3$ and $3$ .

$\frac{{(- 3 x^{6})}^{2}}{5 x^{6} \cdot 3}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $- 3 x^{6}$ .

$\frac{{(- 3)}^{2} {(x^{6})}^{2}}{5 x^{6} \cdot 3}$

Step 2.2

Raise $- 3$ to the power of $2$ .

$\frac{9 {(x^{6})}^{2}}{5 x^{6} \cdot 3}$

Step 2.3

Multiply the exponents in ${(x^{6})}^{2}$ .

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Step 2.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{9 x^{6 \cdot 2}}{5 x^{6} \cdot 3}$

Step 2.3.2

Multiply $6$ by $2$ .

$\frac{9 x^{12}}{5 x^{6} \cdot 3}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply $3$ by $5$ .

$\frac{9 x^{12}}{15 x^{6}}$

Step 3.2

Cancel the common factor of $9$ and $15$ .

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Step 3.2.1

Factor $3$ out of $9 x^{12}$ .

$\frac{3 (3 x^{12})}{15 x^{6}}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $3$ out of $15 x^{6}$ .

$\frac{3 (3 x^{12})}{3 (5 x^{6})}$

Step 3.2.2.2

Cancel the common factor.

$\frac{3 (3 x^{12})}{3 (5 x^{6})}$

Step 3.2.2.3

Rewrite the expression.

$\frac{3 x^{12}}{5 x^{6}}$

Step 3.3

Cancel the common factor of $x^{12}$ and $x^{6}$ .

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Step 3.3.1

Factor $x^{6}$ out of $3 x^{12}$ .

$\frac{x^{6} (3 x^{6})}{5 x^{6}}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $x^{6}$ out of $5 x^{6}$ .

$\frac{x^{6} (3 x^{6})}{x^{6} \cdot 5}$

Step 3.3.2.2

Cancel the common factor.

$\frac{x^{6} (3 x^{6})}{x^{6} \cdot 5}$

Step 3.3.2.3

Rewrite the expression.

$\frac{3 x^{6}}{5}$