Evaluate (42x^-4y^10z^3)/(6x^2y^-2z)

$\frac{42 x^{- 4} y^{10} z^{3}}{6 x^{2} y^{- 2} z}$

Move $x^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{42 y^{10} z^{3}}{6 x^{2} y^{- 2} z x^{4}}$

Multiply $x^{2}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$\frac{42 y^{10} z^{3}}{6 (x^{4} x^{2}) y^{- 2} z}$

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

$\frac{42 y^{10} z^{3}}{6 x^{4 + 2} y^{- 2} z}$

Add $4$ and $2$ .

$\frac{42 y^{10} z^{3}}{6 x^{6} y^{- 2} z}$

Move $y^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{42 y^{10} z^{3} y^{2}}{6 x^{6} z}$

Multiply $y^{10}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$\frac{42 (y^{2} y^{10}) z^{3}}{6 x^{6} z}$

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

$\frac{42 y^{2 + 10} z^{3}}{6 x^{6} z}$

Add $2$ and $10$ .

$\frac{42 y^{12} z^{3}}{6 x^{6} z}$

Cancel the common factor of $42$ and $6$ .

Factor $6$ out of $42 y^{12} z^{3}$ .

$\frac{6 (7 y^{12} z^{3})}{6 x^{6} z}$

Cancel the common factors.

Factor $6$ out of $6 x^{6} z$ .

$\frac{6 (7 y^{12} z^{3})}{6 (x^{6} z)}$

Cancel the common factor.

$\frac{6 (7 y^{12} z^{3})}{6 (x^{6} z)}$

Rewrite the expression.

$\frac{7 y^{12} z^{3}}{x^{6} z}$

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

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

$\frac{z (7 y^{12} z^{2})}{x^{6} z}$

Cancel the common factors.

Factor $z$ out of $x^{6} z$ .

$\frac{z (7 y^{12} z^{2})}{z x^{6}}$

Cancel the common factor.

$\frac{z (7 y^{12} z^{2})}{z x^{6}}$

Rewrite the expression.

$\frac{7 y^{12} z^{2}}{x^{6}}$