Simplify x^4y^2xy^-7x^-3

$x^{4} y^{2} \cdot x y^{- 7} \cdot x^{- 3}$

Step 1

Multiply $x^{4}$ by $x$ by adding the exponents.

Move $x$ .

$x \cdot x^{4} y^{2} \cdot y^{- 7} \cdot x^{- 3}$

Multiply $x$ by $x^{4}$ .

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

$x^{1} x^{4} y^{2} \cdot y^{- 7} \cdot x^{- 3}$

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

$x^{1 + 4} y^{2} \cdot y^{- 7} \cdot x^{- 3}$

Add $1$ and $4$ .

$x^{5} y^{2} \cdot y^{- 7} \cdot x^{- 3}$

Step 2

Multiply $x^{5}$ by $x^{- 3}$ by adding the exponents.

Move $x^{- 3}$ .

$x^{- 3} x^{5} y^{2} \cdot y^{- 7}$

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

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

Add $- 3$ and $5$ .

$x^{2} y^{2} \cdot y^{- 7}$

Step 3

Multiply $y^{2}$ by $y^{- 7}$ by adding the exponents.

Move $y^{- 7}$ .

$x^{2} (y^{- 7} y^{2})$

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

$x^{2} y^{- 7 + 2}$

Add $- 7$ and $2$ .

$x^{2} y^{- 5}$

Step 4

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

$x^{2} \frac{1}{y^{5}}$

Step 5

Combine $x^{2}$ and $\frac{1}{y^{5}}$ .

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

Simplify x^4y^2*xy^-7*x^-3