Algebra Examples

$5 x^{- 5} y^{2} {(2 x^{- 14})}^{2}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$5 \frac{1}{x^{5}} y^{2} {(2 x^{- 14})}^{2}$

Step 2

Combine $5$ and $\frac{1}{x^{5}}$ .

$\frac{5}{x^{5}} y^{2} {(2 x^{- 14})}^{2}$

Step 3

Combine $\frac{5}{x^{5}}$ and $y^{2}$ .

$\frac{5 y^{2}}{x^{5}} {(2 x^{- 14})}^{2}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{5 y^{2}}{x^{5}} {(2 \frac{1}{x^{14}})}^{2}$

Step 5

Combine fractions.

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Step 5.1

Combine $2$ and $\frac{1}{x^{14}}$ .

$\frac{5 y^{2}}{x^{5}} {(\frac{2}{x^{14}})}^{2}$

Step 5.2

Apply the product rule to $\frac{2}{x^{14}}$ .

$\frac{5 y^{2}}{x^{5}} \cdot \frac{2^{2}}{{(x^{14})}^{2}}$

Step 5.3

Combine.

$\frac{5 y^{2} \cdot 2^{2}}{x^{5} {(x^{14})}^{2}}$

Step 6

Simplify the numerator.

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Step 6.1

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

$\frac{5 y^{2} \cdot 4}{x^{5} {(x^{14})}^{2}}$

Step 6.2

Multiply $4$ by $5$ .

$\frac{20 y^{2}}{x^{5} {(x^{14})}^{2}}$

Step 7

Multiply the exponents in ${(x^{14})}^{2}$ .

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Step 7.1

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

$\frac{20 y^{2}}{x^{5} x^{14 \cdot 2}}$

Step 7.2

Multiply $14$ by $2$ .

$\frac{20 y^{2}}{x^{5} x^{28}}$

Step 8

Multiply $x^{5}$ by $x^{28}$ by adding the exponents.

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Step 8.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{20 y^{2}}{x^{5 + 28}}$

Step 8.2

Add $5$ and $28$ .

$\frac{20 y^{2}}{x^{33}}$