Basic Math Examples

$\frac{{(- 3 c^{3 d})}^{2}}{2 c d^{3}}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $- 3 c^{3 d}$ .

$\frac{{(- 3)}^{2} {(c^{3 d})}^{2}}{2 c d^{3}}$

Step 1.2

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

$\frac{9 {(c^{3 d})}^{2}}{2 c d^{3}}$

Step 1.3

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

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Step 1.3.1

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

$\frac{9 c^{3 d \cdot 2}}{2 c d^{3}}$

Step 1.3.2

Multiply $2$ by $3$ .

$\frac{9 c^{6 d}}{2 c d^{3}}$

$\frac{9 c^{6 d}}{2 c d^{3}}$

$\frac{9 c^{6 d}}{2 c d^{3}}$

Step 2

Cancel the common factor of $c^{6 d}$ and $c$ .

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Step 2.1

Factor $c$ out of $9 c^{6 d}$ .

$\frac{c (9 c^{6 d - 1})}{2 c d^{3}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $c$ out of $2 c d^{3}$ .

$\frac{c (9 c^{6 d - 1})}{c (2 d^{3})}$

Step 2.2.2

Cancel the common factor.

$\frac{c (9 c^{6 d - 1})}{c (2 d^{3})}$

Step 2.2.3

Rewrite the expression.

$\frac{9 c^{6 d - 1}}{2 d^{3}}$

$\frac{9 c^{6 d - 1}}{2 d^{3}}$

$\frac{9 c^{6 d - 1}}{2 d^{3}}$

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