Solve (frac{x^{3}*y^{4}*z^2}{x^-7z^-2})^-5

$$( \frac { x ^ { 3 } \cdot y ^ { 4 } \cdot z ^ { 2 } } { x ^ { - 7 } z ^ { - 2 } } ) ^ { - 5 }$$

Evaluate

$$\frac{1}{x^{50}\left(yz\right)^{20}}$$

Solution Steps

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

$$\left(y^{4}z^{4}x^{10}\right)^{-5}$$

Expand \left(y^{4}z^{4}x^{10}\right)^{-5}.

$$\left(y^{4}\right)^{-5}\left(z^{4}\right)^{-5}\left(x^{10}\right)^{-5}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -5 to get -20.

$$y^{-20}\left(z^{4}\right)^{-5}\left(x^{10}\right)^{-5}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -5 to get -20.

$$y^{-20}z^{-20}\left(x^{10}\right)^{-5}$$

To raise a power to another power, multiply the exponents. Multiply 10 and -5 to get -50.

$$y^{-20}z^{-20}x^{-50}$$

Expand

$$\frac{1}{x^{50}\left(yz\right)^{20}}$$

Solution Steps

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

$$\left(y^{4}z^{4}x^{10}\right)^{-5}$$

Expand \left(y^{4}z^{4}x^{10}\right)^{-5}.

$$\left(y^{4}\right)^{-5}\left(z^{4}\right)^{-5}\left(x^{10}\right)^{-5}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -5 to get -20.

$$y^{-20}\left(z^{4}\right)^{-5}\left(x^{10}\right)^{-5}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -5 to get -20.

$$y^{-20}z^{-20}\left(x^{10}\right)^{-5}$$

To raise a power to another power, multiply the exponents. Multiply 10 and -5 to get -50.

$$y^{-20}z^{-20}x^{-50}$$