Algebra Examples

$(\frac{3}{2} x^{- 7}) {(2 x^{- 1})}^{5}$

Step 1

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

$\frac{3}{2} \cdot \frac{1}{x^{7}} {(2 x^{- 1})}^{5}$

Step 2

Combine.

$\frac{3 \cdot 1}{2 x^{7}} {(2 x^{- 1})}^{5}$

Step 3

Multiply $3$ by $1$ .

$\frac{3}{2 x^{7}} {(2 x^{- 1})}^{5}$

Step 4

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

$\frac{3}{2 x^{7}} {(2 \frac{1}{x})}^{5}$

Step 5

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

$\frac{3}{2 x^{7}} {(\frac{2}{x})}^{5}$

Step 6

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

$\frac{3}{2 x^{7}} \cdot \frac{2^{5}}{x^{5}}$

Step 7

Combine.

$\frac{3 \cdot 2^{5}}{2 x^{7} x^{5}}$

Step 8

Multiply $x^{7}$ by $x^{5}$ by adding the exponents.

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Step 8.1

Move $x^{5}$ .

$\frac{3 \cdot 2^{5}}{2 (x^{5} x^{7})}$

Step 8.2

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

$\frac{3 \cdot 2^{5}}{2 x^{5 + 7}}$

Step 8.3

Add $5$ and $7$ .

$\frac{3 \cdot 2^{5}}{2 x^{12}}$

Step 9

Cancel the common factor of $2^{5}$ and $2$ .

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Step 9.1

Factor $2$ out of $3 \cdot 2^{5}$ .

$\frac{2 (3 \cdot 2^{4})}{2 x^{12}}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $2$ out of $2 x^{12}$ .

$\frac{2 (3 \cdot 2^{4})}{2 (x^{12})}$

Step 9.2.2

Cancel the common factor.

$\frac{2 (3 \cdot 2^{4})}{2 x^{12}}$

Step 9.2.3

Rewrite the expression.

$\frac{3 \cdot 2^{4}}{x^{12}}$

Step 10

Simplify the expression.

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Step 10.1

Raise $2$ to the power of $4$ .

$\frac{3 \cdot 16}{x^{12}}$

Step 10.2

Multiply $3$ by $16$ .

$\frac{48}{x^{12}}$