Simplify 6x1/(x^-5)x^-2

$6 x \cdot \frac{1}{x^{- 5}} \cdot x^{- 2}$

Step 1

Multiply $x$ by $x^{- 2}$ by adding the exponents.

Move $x^{- 2}$ .

$6 (x^{- 2} x) \cdot \frac{1}{x^{- 5}}$

Multiply $x^{- 2}$ by $x$ .

Raise $x$ to the power of $1$ .

$6 (x^{- 2} x^{1}) \cdot \frac{1}{x^{- 5}}$

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

$6 x^{- 2 + 1} \cdot \frac{1}{x^{- 5}}$

Add $- 2$ and $1$ .

$6 x^{- 1} \cdot \frac{1}{x^{- 5}}$

Step 2

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

$6 x^{- 1} \cdot \frac{1}{\frac{1}{x^{5}}}$

Step 3

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

$6 \frac{1}{x} \cdot \frac{1}{\frac{1}{x^{5}}}$

Step 4

Combine $6$ and $\frac{1}{x}$ .

$\frac{6}{x} \cdot \frac{1}{\frac{1}{x^{5}}}$

Step 5

Combine.

$\frac{6 \cdot 1}{x \frac{1}{x^{5}}}$

Step 6

Multiply $6$ by $1$ .

$\frac{6}{x \frac{1}{x^{5}}}$

Step 7

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

$\frac{6}{\frac{x}{x^{5}}}$

Step 8

Reduce the expression $\frac{x}{x^{5}}$ by cancelling the common factors.

Raise $x$ to the power of $1$ .

$\frac{6}{\frac{x^{1}}{x^{5}}}$

Factor $x$ out of $x^{1}$ .

$\frac{6}{\frac{x \cdot 1}{x^{5}}}$

Factor $x$ out of $x^{5}$ .

$\frac{6}{\frac{x \cdot 1}{x \cdot x^{4}}}$

Cancel the common factor.

$\frac{6}{\frac{x \cdot 1}{x \cdot x^{4}}}$

Rewrite the expression.

$\frac{6}{\frac{1}{x^{4}}}$

Step 9

Multiply the numerator by the reciprocal of the denominator.

$6 x^{4}$

Simplify 6x*1/(x^-5)*x^-2

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Simplify 6x1/(x^-5)x^-2