Algebra Examples

${(\frac{c^{2} d^{- 2}}{c})}^{5}$

Step 1

Move $d^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{c^{2}}{c d^{2}})}^{5}$

Step 2

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

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Step 2.1

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

${(\frac{c \cdot c}{c d^{2}})}^{5}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

${(\frac{c \cdot c}{c (d^{2})})}^{5}$

Step 2.2.2

Cancel the common factor.

${(\frac{c \cdot c}{c d^{2}})}^{5}$

Step 2.2.3

Rewrite the expression.

${(\frac{c}{d^{2}})}^{5}$

Step 3

Apply basic rules of exponents.

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Step 3.1

Apply the product rule to $\frac{c}{d^{2}}$ .

$\frac{c^{5}}{{(d^{2})}^{5}}$

Step 3.2

Multiply the exponents in ${(d^{2})}^{5}$ .

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Step 3.2.1

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

$\frac{c^{5}}{d^{2 \cdot 5}}$

Step 3.2.2

Multiply $2$ by $5$ .

$\frac{c^{5}}{d^{10}}$