Algebra Examples

$\frac{20 x^{- 3} c}{{(4 x^{4})}^{- 5}}$

Step 1

Move $x^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{20 c}{{(4 x^{4})}^{- 5} x^{3}}$

Step 2

Move ${(4 x^{4})}^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{20 c {(4 x^{4})}^{5}}{x^{3}}$

Step 3

Simplify the numerator.

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Step 3.1

Apply the product rule to $4 x^{4}$ .

$\frac{20 c \cdot 4^{5} {(x^{4})}^{5}}{x^{3}}$

Step 3.2

Raise $4$ to the power of $5$ .

$\frac{20 c \cdot 1024 {(x^{4})}^{5}}{x^{3}}$

Step 3.3

Multiply the exponents in ${(x^{4})}^{5}$ .

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Step 3.3.1

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

$\frac{20 c \cdot 1024 x^{4 \cdot 5}}{x^{3}}$

Step 3.3.2

Multiply $4$ by $5$ .

$\frac{20 c \cdot 1024 x^{20}}{x^{3}}$

Step 3.4

Multiply $1024$ by $20$ .

$\frac{20480 c x^{20}}{x^{3}}$

Step 4

Cancel the common factor of $x^{20}$ and $x^{3}$ .

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Step 4.1

Factor $x^{3}$ out of $20480 c x^{20}$ .

$\frac{x^{3} (20480 c x^{17})}{x^{3}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Multiply by $1$ .

$\frac{x^{3} (20480 c x^{17})}{x^{3} \cdot 1}$

Step 4.2.2

Cancel the common factor.

$\frac{x^{3} (20480 c x^{17})}{x^{3} \cdot 1}$

Step 4.2.3

Rewrite the expression.

$\frac{20480 c x^{17}}{1}$

Step 4.2.4

Divide $20480 c x^{17}$ by $1$ .

$20480 c x^{17}$