Solve (frac{16c^{6}c^-2}{(2c^2)^3})^-1=

$$( \frac { 16 c ^ { 6 } c ^ { - 2 } } { ( 2 c ^ { 2 } ) ^ { 3 } } ) ^ { - 1 } =$$

Evaluate

$$\frac{c^{2}}{2}$$

Solution Steps

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

$$\left(\frac{16c^{4}}{\left(2c^{2}\right)^{3}}\right)^{-1}$$

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

$$\left(\frac{16c^{4}}{2^{3}\left(c^{2}\right)^{3}}\right)^{-1}$$

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

$$\left(\frac{16c^{4}}{2^{3}c^{6}}\right)^{-1}$$

Calculate 2 to the power of 3 and get 8.

$$\left(\frac{16c^{4}}{8c^{6}}\right)^{-1}$$

Cancel out 8c^{4} in both numerator and denominator.

$$\left(\frac{2}{c^{2}}\right)^{-1}$$

To raise \frac{2}{c^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{2^{-1}}{\left(c^{2}\right)^{-1}}$$

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

$$\frac{2^{-1}}{c^{-2}}$$

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

$$\frac{\frac{1}{2}}{c^{-2}}$$

Express \frac{\frac{1}{2}}{c^{-2}} as a single fraction.

$$\frac{1}{2c^{-2}}$$

Expand

$$\frac{c^{2}}{2}$$

Solution Steps

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

$$\left(\frac{16c^{4}}{\left(2c^{2}\right)^{3}}\right)^{-1}$$

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

$$\left(\frac{16c^{4}}{2^{3}\left(c^{2}\right)^{3}}\right)^{-1}$$

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

$$\left(\frac{16c^{4}}{2^{3}c^{6}}\right)^{-1}$$

Calculate 2 to the power of 3 and get 8.

$$\left(\frac{16c^{4}}{8c^{6}}\right)^{-1}$$

Cancel out 8c^{4} in both numerator and denominator.

$$\left(\frac{2}{c^{2}}\right)^{-1}$$

To raise \frac{2}{c^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{2^{-1}}{\left(c^{2}\right)^{-1}}$$

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

$$\frac{2^{-1}}{c^{-2}}$$

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

$$\frac{\frac{1}{2}}{c^{-2}}$$

Express \frac{\frac{1}{2}}{c^{-2}} as a single fraction.

$$\frac{1}{2c^{-2}}$$