Basic Math Examples

${(3 e^{2} f)}^{3} \div 18 e^{2} f^{3}$

Step 1

Rewrite the division as a fraction.

$\frac{{(3 e^{2} f)}^{3}}{18 e^{2} f^{3}}$

Step 2

Simplify the numerator.

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Step 2.1

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

$\frac{{(3 e^{2})}^{3} f^{3}}{18 e^{2} f^{3}}$

Step 2.2

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

$\frac{3^{3} {(e^{2})}^{3} f^{3}}{18 e^{2} f^{3}}$

Step 2.3

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

$\frac{27 {(e^{2})}^{3} f^{3}}{18 e^{2} f^{3}}$

Step 2.4

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

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Step 2.4.1

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

$\frac{27 e^{2 \cdot 3} f^{3}}{18 e^{2} f^{3}}$

Step 2.4.2

Multiply $2$ by $3$ .

$\frac{27 e^{6} f^{3}}{18 e^{2} f^{3}}$

$\frac{27 e^{6} f^{3}}{18 e^{2} f^{3}}$

$\frac{27 e^{6} f^{3}}{18 e^{2} f^{3}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $27$ and $18$ .

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Step 3.1.1

Factor $9$ out of $27 e^{6} f^{3}$ .

$\frac{9 (3 e^{6} f^{3})}{18 e^{2} f^{3}}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $9$ out of $18 e^{2} f^{3}$ .

$\frac{9 (3 e^{6} f^{3})}{9 (2 e^{2} f^{3})}$

Step 3.1.2.2

Cancel the common factor.

$\frac{9 (3 e^{6} f^{3})}{9 (2 e^{2} f^{3})}$

Step 3.1.2.3

Rewrite the expression.

$\frac{3 e^{6} f^{3}}{2 e^{2} f^{3}}$

$\frac{3 e^{6} f^{3}}{2 e^{2} f^{3}}$

$\frac{3 e^{6} f^{3}}{2 e^{2} f^{3}}$

Step 3.2

Cancel the common factor of $e^{6}$ and $e^{2}$ .

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Step 3.2.1

Factor $e^{2}$ out of $3 e^{6} f^{3}$ .

$\frac{e^{2} (3 e^{4} f^{3})}{2 e^{2} f^{3}}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $e^{2}$ out of $2 e^{2} f^{3}$ .

$\frac{e^{2} (3 e^{4} f^{3})}{e^{2} (2 f^{3})}$

Step 3.2.2.2

Cancel the common factor.

$\frac{e^{2} (3 e^{4} f^{3})}{e^{2} (2 f^{3})}$

Step 3.2.2.3

Rewrite the expression.

$\frac{3 e^{4} f^{3}}{2 f^{3}}$

$\frac{3 e^{4} f^{3}}{2 f^{3}}$

$\frac{3 e^{4} f^{3}}{2 f^{3}}$

Step 3.3

Cancel the common factor of $f^{3}$ .

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Step 3.3.1

Cancel the common factor.

$\frac{3 e^{4} f^{3}}{2 f^{3}}$

Step 3.3.2

Rewrite the expression.

$\frac{3 e^{4}}{2}$

$\frac{3 e^{4}}{2}$

$\frac{3 e^{4}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{3 e^{4}}{2}$

Decimal Form:

$81.89722504 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$