Solve (-2r^{-4})^2(-3r^2z^8)^-1

$$( - 2 r ^ { - 4 } ) ^ { 2 } ( - 3 r ^ { 2 } z ^ { 8 } ) ^ { - 1 }$$

Evaluate

$$-\frac{4}{3z^{8}r^{10}}$$

Solution Steps

Expand \left(-2r^{-4}\right)^{2}.

$$\left(-2\right)^{2}\left(r^{-4}\right)^{2}\left(-3r^{2}z^{8}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply -4 and 2 to get -8.

$$\left(-2\right)^{2}r^{-8}\left(-3r^{2}z^{8}\right)^{-1}$$

Calculate -2 to the power of 2 and get 4.

$$4r^{-8}\left(-3r^{2}z^{8}\right)^{-1}$$

Expand \left(-3r^{2}z^{8}\right)^{-1}.

$$4r^{-8}\left(-3\right)^{-1}\left(r^{2}\right)^{-1}\left(z^{8}\right)^{-1}$$

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

$$4r^{-8}\left(-3\right)^{-1}r^{-2}\left(z^{8}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply 8 and -1 to get -8.

$$4r^{-8}\left(-3\right)^{-1}r^{-2}z^{-8}$$

Calculate -3 to the power of -1 and get -\frac{1}{3}.

$$4r^{-8}\left(-\frac{1}{3}\right)r^{-2}z^{-8}$$

Multiply 4 and -\frac{1}{3} to get -\frac{4}{3}.

$$-\frac{4}{3}r^{-8}r^{-2}z^{-8}$$

To multiply powers of the same base, add their exponents. Add -8 and -2 to get -10.

$$-\frac{4}{3}r^{-10}z^{-8}$$

Expand

$$-\frac{4}{3z^{8}r^{10}}$$

Solution Steps

Expand \left(-2r^{-4}\right)^{2}.

$$\left(-2\right)^{2}\left(r^{-4}\right)^{2}\left(-3r^{2}z^{8}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply -4 and 2 to get -8.

$$\left(-2\right)^{2}r^{-8}\left(-3r^{2}z^{8}\right)^{-1}$$

Calculate -2 to the power of 2 and get 4.

$$4r^{-8}\left(-3r^{2}z^{8}\right)^{-1}$$

Expand \left(-3r^{2}z^{8}\right)^{-1}.

$$4r^{-8}\left(-3\right)^{-1}\left(r^{2}\right)^{-1}\left(z^{8}\right)^{-1}$$

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

$$4r^{-8}\left(-3\right)^{-1}r^{-2}\left(z^{8}\right)^{-1}$$

To raise a power to another power, multiply the exponents. Multiply 8 and -1 to get -8.

$$4r^{-8}\left(-3\right)^{-1}r^{-2}z^{-8}$$

Calculate -3 to the power of -1 and get -\frac{1}{3}.

$$4r^{-8}\left(-\frac{1}{3}\right)r^{-2}z^{-8}$$

Multiply 4 and -\frac{1}{3} to get -\frac{4}{3}.

$$-\frac{4}{3}r^{-8}r^{-2}z^{-8}$$

To multiply powers of the same base, add their exponents. Add -8 and -2 to get -10.

$$-\frac{4}{3}r^{-10}z^{-8}$$