Algebra Examples

$\frac{{(6 x^{3})}^{2}}{{(2 x^{2})}^{3}} \cdot {(3 x^{2})}^{0}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{6^{2} {(x^{3})}^{2}}{{(2 x^{2})}^{3}} \cdot {(3 x^{2})}^{0}$

Step 1.2

Raise $6$ to the power of $2$ .

$\frac{36 {(x^{3})}^{2}}{{(2 x^{2})}^{3}} \cdot {(3 x^{2})}^{0}$

Step 1.3

Multiply the exponents in ${(x^{3})}^{2}$ .

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Step 1.3.1

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

$\frac{36 x^{3 \cdot 2}}{{(2 x^{2})}^{3}} \cdot {(3 x^{2})}^{0}$

Step 1.3.2

Multiply $3$ by $2$ .

$\frac{36 x^{6}}{{(2 x^{2})}^{3}} \cdot {(3 x^{2})}^{0}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $2 x^{2}$ .

$\frac{36 x^{6}}{2^{3} {(x^{2})}^{3}} \cdot {(3 x^{2})}^{0}$

Step 2.2

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

$\frac{36 x^{6}}{8 {(x^{2})}^{3}} \cdot {(3 x^{2})}^{0}$

Step 2.3

Multiply the exponents in ${(x^{2})}^{3}$ .

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Step 2.3.1

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

$\frac{36 x^{6}}{8 x^{2 \cdot 3}} \cdot {(3 x^{2})}^{0}$

Step 2.3.2

Multiply $2$ by $3$ .

$\frac{36 x^{6}}{8 x^{6}} \cdot {(3 x^{2})}^{0}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $36$ and $8$ .

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Step 3.1.1

Factor $4$ out of $36 x^{6}$ .

$\frac{4 (9 x^{6})}{8 x^{6}} \cdot {(3 x^{2})}^{0}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $4$ out of $8 x^{6}$ .

$\frac{4 (9 x^{6})}{4 (2 x^{6})} \cdot {(3 x^{2})}^{0}$

Step 3.1.2.2

Cancel the common factor.

$\frac{4 (9 x^{6})}{4 (2 x^{6})} \cdot {(3 x^{2})}^{0}$

Step 3.1.2.3

Rewrite the expression.

$\frac{9 x^{6}}{2 x^{6}} \cdot {(3 x^{2})}^{0}$

Step 3.2

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

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Step 3.2.1

Cancel the common factor.

$\frac{9 x^{6}}{2 x^{6}} \cdot {(3 x^{2})}^{0}$

Step 3.2.2

Rewrite the expression.

$\frac{9}{2} \cdot {(3 x^{2})}^{0}$

Step 3.3

Simplify the expression.

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Step 3.3.1

Apply the product rule to $3 x^{2}$ .

$\frac{9}{2} \cdot (3^{0} {(x^{2})}^{0})$

Step 3.3.2

Anything raised to $0$ is $1$ .

$\frac{9}{2} \cdot (1 {(x^{2})}^{0})$

Step 3.3.3

Multiply ${(x^{2})}^{0}$ by $1$ .

$\frac{9}{2} \cdot {(x^{2})}^{0}$

Step 3.3.4

Multiply the exponents in ${(x^{2})}^{0}$ .

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Step 3.3.4.1

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

$\frac{9}{2} \cdot x^{2 \cdot 0}$

Step 3.3.4.2

Multiply $2$ by $0$ .

$\frac{9}{2} \cdot x^{0}$

Step 3.3.5

Anything raised to $0$ is $1$ .

$\frac{9}{2} \cdot 1$

Step 3.3.6

Multiply $\frac{9}{2}$ by $1$ .

$\frac{9}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{2}$

Decimal Form:

$4.5$

Mixed Number Form:

$4 \frac{1}{2}$