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:

$4 \frac{1}{2}$