Solve (2r^-2)^3(4^-1r)^2

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

Evaluate

$$\frac{1}{2r^{4}}$$

Solution Steps

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

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

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

$$2^{3}r^{-6}\times \left(4^{-1}r\right)^{2}$$

Calculate 2 to the power of 3 and get 8.

$$8r^{-6}\times \left(4^{-1}r\right)^{2}$$

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

$$8r^{-6}\times \left(\frac{1}{4}r\right)^{2}$$

Expand \left(\frac{1}{4}r\right)^{2}.

$$8r^{-6}\times \left(\frac{1}{4}\right)^{2}r^{2}$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$8r^{-6}\times \frac{1}{16}r^{2}$$

Multiply 8 and \frac{1}{16} to get \frac{1}{2}.

$$\frac{1}{2}r^{-6}r^{2}$$

To multiply powers of the same base, add their exponents. Add -6 and 2 to get -4.

$$\frac{1}{2}r^{-4}$$

Expand

$$\frac{1}{2r^{4}}$$

Solution Steps

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

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

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

$$2^{3}r^{-6}\times \left(4^{-1}r\right)^{2}$$

Calculate 2 to the power of 3 and get 8.

$$8r^{-6}\times \left(4^{-1}r\right)^{2}$$

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

$$8r^{-6}\times \left(\frac{1}{4}r\right)^{2}$$

Expand \left(\frac{1}{4}r\right)^{2}.

$$8r^{-6}\times \left(\frac{1}{4}\right)^{2}r^{2}$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$8r^{-6}\times \frac{1}{16}r^{2}$$

Multiply 8 and \frac{1}{16} to get \frac{1}{2}.

$$\frac{1}{2}r^{-6}r^{2}$$

To multiply powers of the same base, add their exponents. Add -6 and 2 to get -4.

$$\frac{1}{2}r^{-4}$$