Solve (frac{2x^{3}u}{z^-1})^-2(x^-2z^7)

$$( \frac { 2 x ^ { 3 } u } { z ^ { - 1 } } ) ^ { - 2 } ( x ^ { - 2 } z ^ { 7 } )$$

Evaluate

$$\frac{z^{5}}{4u^{2}x^{8}}$$

Solution Steps

To raise \frac{2x^{3}u}{z^{-1}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2x^{3}u\right)^{-2}}{\left(z^{-1}\right)^{-2}}x^{-2}z^{7}$$

Express \frac{\left(2x^{3}u\right)^{-2}}{\left(z^{-1}\right)^{-2}}x^{-2} as a single fraction.

$$\frac{\left(2x^{3}u\right)^{-2}x^{-2}}{\left(z^{-1}\right)^{-2}}z^{7}$$

Express \frac{\left(2x^{3}u\right)^{-2}x^{-2}}{\left(z^{-1}\right)^{-2}}z^{7} as a single fraction.

$$\frac{\left(2x^{3}u\right)^{-2}x^{-2}z^{7}}{\left(z^{-1}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -2 to get 2.

$$\frac{\left(2x^{3}u\right)^{-2}x^{-2}z^{7}}{z^{2}}$$

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

$$\left(2ux^{3}\right)^{-2}x^{-2}z^{5}$$

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

$$2^{-2}u^{-2}\left(x^{3}\right)^{-2}x^{-2}z^{5}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.

$$2^{-2}u^{-2}x^{-6}x^{-2}z^{5}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{1}{4}u^{-2}x^{-6}x^{-2}z^{5}$$

To multiply powers of the same base, add their exponents. Add -6 and -2 to get -8.

$$\frac{1}{4}u^{-2}x^{-8}z^{5}$$

Expand

$$\frac{z^{5}}{4u^{2}x^{8}}$$

Solution Steps

To raise \frac{2x^{3}u}{z^{-1}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2x^{3}u\right)^{-2}}{\left(z^{-1}\right)^{-2}}x^{-2}z^{7}$$

Express \frac{\left(2x^{3}u\right)^{-2}}{\left(z^{-1}\right)^{-2}}x^{-2} as a single fraction.

$$\frac{\left(2x^{3}u\right)^{-2}x^{-2}}{\left(z^{-1}\right)^{-2}}z^{7}$$

Express \frac{\left(2x^{3}u\right)^{-2}x^{-2}}{\left(z^{-1}\right)^{-2}}z^{7} as a single fraction.

$$\frac{\left(2x^{3}u\right)^{-2}x^{-2}z^{7}}{\left(z^{-1}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -2 to get 2.

$$\frac{\left(2x^{3}u\right)^{-2}x^{-2}z^{7}}{z^{2}}$$

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

$$\left(2ux^{3}\right)^{-2}x^{-2}z^{5}$$

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

$$2^{-2}u^{-2}\left(x^{3}\right)^{-2}x^{-2}z^{5}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.

$$2^{-2}u^{-2}x^{-6}x^{-2}z^{5}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{1}{4}u^{-2}x^{-6}x^{-2}z^{5}$$

To multiply powers of the same base, add their exponents. Add -6 and -2 to get -8.

$$\frac{1}{4}u^{-2}x^{-8}z^{5}$$