Simplify (4x^-2(yz)^-1)/(2^3x^4y)

$\frac{4 x^{- 2} {(y z)}^{- 1}}{2^{3} x^{4} y}$

Step 1

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

$\frac{4 {(y z)}^{- 1}}{2^{3} x^{4} y x^{2}}$

Step 2

Move ${(y z)}^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 3

Simplify the denominator.

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

Move $x^{2}$ .

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

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

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

Add $2$ and $4$ .

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

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$\frac{4}{2^{3} x^{6} (y \cdot y) z}$

Multiply $y$ by $y$ .

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

Step 4

Raise $2$ to the power of $3$ .

$\frac{4}{8 x^{6} y^{2} z}$

Step 5

Cancel the common factor of $4$ and $8$ .

Factor $4$ out of $4$ .

$\frac{4 (1)}{8 x^{6} y^{2} z}$

Cancel the common factors.

Factor $4$ out of $8 x^{6} y^{2} z$ .

$\frac{4 (1)}{4 (2 x^{6} y^{2} z)}$

Cancel the common factor.

$\frac{4 \cdot 1}{4 (2 x^{6} y^{2} z)}$

Rewrite the expression.

$\frac{1}{2 x^{6} y^{2} z}$