Simplify x^-9y^10z^7*yx^4

$x^{- 9} y^{10} z^{7} \cdot y x^{4}$

Step 1

Multiply $x^{- 9}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$x^{4} x^{- 9} y^{10} z^{7} \cdot y$

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

$x^{4 - 9} y^{10} z^{7} \cdot y$

Subtract $9$ from $4$ .

$x^{- 5} y^{10} z^{7} \cdot y$

Step 2

Multiply $y^{10}$ by $y$ by adding the exponents.

Move $y$ .

$x^{- 5} (y \cdot y^{10}) z^{7}$

Multiply $y$ by $y^{10}$ .

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

$x^{- 5} (y^{1} y^{10}) z^{7}$

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

$x^{- 5} y^{1 + 10} z^{7}$

Add $1$ and $10$ .

$x^{- 5} y^{11} z^{7}$

Step 3

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

$\frac{1}{x^{5}} y^{11} z^{7}$

Step 4

Combine $\frac{1}{x^{5}}$ and $y^{11}$ .

$\frac{y^{11}}{x^{5}} z^{7}$

Step 5

Combine $\frac{y^{11}}{x^{5}}$ and $z^{7}$ .

$\frac{y^{11} z^{7}}{x^{5}}$