Simplify (10x^-3y^4z^2)/(5x^-4y^3)

$\frac{10 x^{- 3} y^{4} z^{2}}{5 x^{- 4} y^{3}}$

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

$\frac{10 x^{- 3} y^{4} z^{2} x^{4}}{5 y^{3}}$

Simplify the numerator.

Multiply $x^{- 3}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$\frac{10 (x^{4} x^{- 3}) y^{4} z^{2}}{5 y^{3}}$

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

$\frac{10 x^{4 - 3} y^{4} z^{2}}{5 y^{3}}$

Subtract $3$ from $4$ .

$\frac{10 x^{1} y^{4} z^{2}}{5 y^{3}}$

Simplify $10 x^{1} y^{4} z^{2}$ .

$\frac{10 x y^{4} z^{2}}{5 y^{3}}$

Cancel the common factor of $10$ and $5$ .

Factor $5$ out of $10 x y^{4} z^{2}$ .

$\frac{5 (2 x y^{4} z^{2})}{5 y^{3}}$

Cancel the common factors.

Factor $5$ out of $5 y^{3}$ .

$\frac{5 (2 x y^{4} z^{2})}{5 (y^{3})}$

Cancel the common factor.

$\frac{5 (2 x y^{4} z^{2})}{5 y^{3}}$

Rewrite the expression.

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

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

Factor $y^{3}$ out of $2 x y^{4} z^{2}$ .

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

Cancel the common factors.

Multiply by $1$ .

$\frac{y^{3} (2 x y z^{2})}{y^{3} \cdot 1}$

Cancel the common factor.

$\frac{y^{3} (2 x y z^{2})}{y^{3} \cdot 1}$

Rewrite the expression.

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

Divide $2 x y z^{2}$ by $1$ .

$2 x y z^{2}$