Solve frac{(3x^{0}y^{-2}z)^2}{18x^2y^4z^2}

$$\frac { ( 3 x ^ { 0 } y ^ { - 2 } z ) ^ { 2 } } { 18 x ^ { 2 } y ^ { 4 } z ^ { 2 } }$$

Evaluate

$$\frac{1}{2x^{2}y^{8}}$$

Solution Steps

Calculate x to the power of 0 and get 1.

$$\frac{\left(3\times 1y^{-2}z\right)^{2}}{18x^{2}y^{4}z^{2}}$$

Multiply 3 and 1 to get 3.

$$\frac{\left(3y^{-2}z\right)^{2}}{18x^{2}y^{4}z^{2}}$$

Expand \left(3y^{-2}z\right)^{2}.

$$\frac{3^{2}\left(y^{-2}\right)^{2}z^{2}}{18x^{2}y^{4}z^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 2 to get -4.

$$\frac{3^{2}y^{-4}z^{2}}{18x^{2}y^{4}z^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9y^{-4}z^{2}}{18x^{2}y^{4}z^{2}}$$

Cancel out 9z^{2} in both numerator and denominator.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{1}{2x^{2}y^{8}}$$

Expand

$$\frac{1}{2x^{2}y^{8}}$$

Solution Steps

Calculate x to the power of 0 and get 1.

$$\frac{\left(3\times 1y^{-2}z\right)^{2}}{18x^{2}y^{4}z^{2}}$$

Multiply 3 and 1 to get 3.

$$\frac{\left(3y^{-2}z\right)^{2}}{18x^{2}y^{4}z^{2}}$$

Expand \left(3y^{-2}z\right)^{2}.

$$\frac{3^{2}\left(y^{-2}\right)^{2}z^{2}}{18x^{2}y^{4}z^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 2 to get -4.

$$\frac{3^{2}y^{-4}z^{2}}{18x^{2}y^{4}z^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9y^{-4}z^{2}}{18x^{2}y^{4}z^{2}}$$

Cancel out 9z^{2} in both numerator and denominator.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{1}{2x^{2}y^{8}}$$