Simplify 3x1/(x^-4)x^-3

$3 x \cdot \frac{1}{x^{- 4}} \cdot x^{- 3}$

Step 1

Multiply $x$ by $x^{- 3}$ by adding the exponents.

Move $x^{- 3}$ .

$3 (x^{- 3} x) \cdot \frac{1}{x^{- 4}}$

Multiply $x^{- 3}$ by $x$ .

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

$3 (x^{- 3} x^{1}) \cdot \frac{1}{x^{- 4}}$

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

$3 x^{- 3 + 1} \cdot \frac{1}{x^{- 4}}$

Add $- 3$ and $1$ .

$3 x^{- 2} \cdot \frac{1}{x^{- 4}}$

Step 2

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

$3 x^{- 2} \cdot \frac{1}{\frac{1}{x^{4}}}$

Step 3

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

$3 \frac{1}{x^{2}} \cdot \frac{1}{\frac{1}{x^{4}}}$

Step 4

Combine $3$ and $\frac{1}{x^{2}}$ .

$\frac{3}{x^{2}} \cdot \frac{1}{\frac{1}{x^{4}}}$

Step 5

Combine.

$\frac{3 \cdot 1}{x^{2} \frac{1}{x^{4}}}$

Step 6

Multiply $3$ by $1$ .

$\frac{3}{x^{2} \frac{1}{x^{4}}}$

Step 7

Combine $x^{2}$ and $\frac{1}{x^{4}}$ .

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

Step 8

Reduce the expression $\frac{x^{2}}{x^{4}}$ by cancelling the common factors.

Multiply by $1$ .

$\frac{3}{\frac{x^{2} \cdot 1}{x^{4}}}$

Factor $x^{2}$ out of $x^{4}$ .

$\frac{3}{\frac{x^{2} \cdot 1}{x^{2} x^{2}}}$

Cancel the common factor.

$\frac{3}{\frac{x^{2} \cdot 1}{x^{2} x^{2}}}$

Rewrite the expression.

$\frac{3}{\frac{1}{x^{2}}}$

Step 9

Multiply the numerator by the reciprocal of the denominator.

$3 x^{2}$

Simplify 3x*1/(x^-4)*x^-3