Simplify (12x^4y^7z^0)/(-3x^3y^9z^-5)

$\frac{12 x^{4} y^{7} z^{0}}{- 3 x^{3} y^{9} z^{- 5}}$

Step 1

Move $z^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{12 x^{4} y^{7} z^{0} z^{5}}{- 3 x^{3} y^{9}}$

Step 2

Multiply $z^{0}$ by $z^{5}$ by adding the exponents.

Move $z^{5}$ .

$\frac{12 x^{4} y^{7} (z^{5} z^{0})}{- 3 x^{3} y^{9}}$

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

$\frac{12 x^{4} y^{7} z^{5 + 0}}{- 3 x^{3} y^{9}}$

Add $5$ and $0$ .

$\frac{12 x^{4} y^{7} z^{5}}{- 3 x^{3} y^{9}}$

Step 3

Cancel the common factor of $12$ and $- 3$ .

Factor $3$ out of $12 x^{4} y^{7} z^{5}$ .

$\frac{3 (4 x^{4} y^{7} z^{5})}{- 3 x^{3} y^{9}}$

Cancel the common factors.

Factor $3$ out of $- 3 x^{3} y^{9}$ .

$\frac{3 (4 x^{4} y^{7} z^{5})}{3 (- x^{3} y^{9})}$

Cancel the common factor.

$\frac{3 (4 x^{4} y^{7} z^{5})}{3 (- x^{3} y^{9})}$

Rewrite the expression.

$\frac{4 x^{4} y^{7} z^{5}}{- x^{3} y^{9}}$

Step 4

Cancel the common factor of $x^{4}$ and $x^{3}$ .

Factor $x^{3}$ out of $4 x^{4} y^{7} z^{5}$ .

$\frac{x^{3} (4 x y^{7} z^{5})}{- x^{3} y^{9}}$

Cancel the common factors.

Factor $x^{3}$ out of $- x^{3} y^{9}$ .

$\frac{x^{3} (4 x y^{7} z^{5})}{x^{3} (- 1 y^{9})}$

Cancel the common factor.

$\frac{x^{3} (4 x y^{7} z^{5})}{x^{3} (- 1 y^{9})}$

Rewrite the expression.

$\frac{4 x y^{7} z^{5}}{- 1 y^{9}}$

Step 5

Cancel the common factor of $y^{7}$ and $y^{9}$ .

Factor $y^{7}$ out of $4 x y^{7} z^{5}$ .

$\frac{y^{7} (4 x z^{5})}{- 1 y^{9}}$

Cancel the common factors.

Factor $y^{7}$ out of $- 1 y^{9}$ .

$\frac{y^{7} (4 x z^{5})}{y^{7} (- 1 y^{2})}$

Cancel the common factor.

$\frac{y^{7} (4 x z^{5})}{y^{7} (- 1 y^{2})}$

Rewrite the expression.

$\frac{4 x z^{5}}{- 1 y^{2}}$

Step 6

Move the negative in front of the fraction.

$- \frac{4 x z^{5}}{y^{2}}$

Simplify (12x^4y^7z^0)/(-3x^3y^9z^-5)

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