Solve frac{(c^{4}d^{-1})^{2}}{(2c^{2})^4}div16/(2c^3d^-5)^4

$$\frac { ( c ^ { 4 } d ^ { - 1 } ) ^ { 2 } } { ( 2 c ^ { 2 } ) ^ { 4 } } \div \frac { 16 } { ( 2 c ^ { 3 } d ^ { - 5 } ) ^ { 4 } }$$

Evaluate

$$\frac{c^{12}}{16d^{22}}$$

Solution Steps

Divide \frac{\left(c^{4}d^{-1}\right)^{2}}{\left(2c^{2}\right)^{4}} by \frac{16}{\left(2c^{3}d^{-5}\right)^{4}} by multiplying \frac{\left(c^{4}d^{-1}\right)^{2}}{\left(2c^{2}\right)^{4}} by the reciprocal of \frac{16}{\left(2c^{3}d^{-5}\right)^{4}}.

$$\frac{\left(c^{4}d^{-1}\right)^{2}\times \left(2c^{3}d^{-5}\right)^{4}}{\left(2c^{2}\right)^{4}\times 16}$$

Expand \left(c^{4}d^{-1}\right)^{2}.

$$\frac{\left(c^{4}\right)^{2}\left(d^{-1}\right)^{2}\times \left(2c^{3}d^{-5}\right)^{4}}{\left(2c^{2}\right)^{4}\times 16}$$

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

$$\frac{c^{8}\left(d^{-1}\right)^{2}\times \left(2c^{3}d^{-5}\right)^{4}}{\left(2c^{2}\right)^{4}\times 16}$$

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

$$\frac{c^{8}d^{-2}\times \left(2c^{3}d^{-5}\right)^{4}}{\left(2c^{2}\right)^{4}\times 16}$$

Expand \left(2c^{3}d^{-5}\right)^{4}.

$$\frac{c^{8}d^{-2}\times 2^{4}\left(c^{3}\right)^{4}\left(d^{-5}\right)^{4}}{\left(2c^{2}\right)^{4}\times 16}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{c^{8}d^{-2}\times 2^{4}c^{12}\left(d^{-5}\right)^{4}}{\left(2c^{2}\right)^{4}\times 16}$$

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

$$\frac{c^{8}d^{-2}\times 2^{4}c^{12}d^{-20}}{\left(2c^{2}\right)^{4}\times 16}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{c^{8}d^{-2}\times 16c^{12}d^{-20}}{\left(2c^{2}\right)^{4}\times 16}$$

To multiply powers of the same base, add their exponents. Add 8 and 12 to get 20.

$$\frac{c^{20}d^{-2}\times 16d^{-20}}{\left(2c^{2}\right)^{4}\times 16}$$

To multiply powers of the same base, add their exponents. Add -2 and -20 to get -22.

$$\frac{c^{20}d^{-22}\times 16}{\left(2c^{2}\right)^{4}\times 16}$$

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

$$\frac{c^{20}d^{-22}\times 16}{2^{4}\left(c^{2}\right)^{4}\times 16}$$

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

$$\frac{c^{20}d^{-22}\times 16}{2^{4}c^{8}\times 16}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{c^{20}d^{-22}\times 16}{16c^{8}\times 16}$$

Multiply 16 and 16 to get 256.

$$\frac{c^{20}d^{-22}\times 16}{256c^{8}}$$

Cancel out 16c^{8} in both numerator and denominator.

$$\frac{d^{-22}c^{12}}{16}$$

Expand

$$\frac{c^{12}}{16d^{22}}$$

Solution Steps

Divide \frac{\left(c^{4}d^{-1}\right)^{2}}{\left(2c^{2}\right)^{4}} by \frac{16}{\left(2c^{3}d^{-5}\right)^{4}} by multiplying \frac{\left(c^{4}d^{-1}\right)^{2}}{\left(2c^{2}\right)^{4}} by the reciprocal of \frac{16}{\left(2c^{3}d^{-5}\right)^{4}}.

$$\frac{\left(c^{4}d^{-1}\right)^{2}\times \left(2c^{3}d^{-5}\right)^{4}}{\left(2c^{2}\right)^{4}\times 16}$$

Expand \left(c^{4}d^{-1}\right)^{2}.

$$\frac{\left(c^{4}\right)^{2}\left(d^{-1}\right)^{2}\times \left(2c^{3}d^{-5}\right)^{4}}{\left(2c^{2}\right)^{4}\times 16}$$

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

$$\frac{c^{8}\left(d^{-1}\right)^{2}\times \left(2c^{3}d^{-5}\right)^{4}}{\left(2c^{2}\right)^{4}\times 16}$$

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

$$\frac{c^{8}d^{-2}\times \left(2c^{3}d^{-5}\right)^{4}}{\left(2c^{2}\right)^{4}\times 16}$$

Expand \left(2c^{3}d^{-5}\right)^{4}.

$$\frac{c^{8}d^{-2}\times 2^{4}\left(c^{3}\right)^{4}\left(d^{-5}\right)^{4}}{\left(2c^{2}\right)^{4}\times 16}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{c^{8}d^{-2}\times 2^{4}c^{12}\left(d^{-5}\right)^{4}}{\left(2c^{2}\right)^{4}\times 16}$$

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

$$\frac{c^{8}d^{-2}\times 2^{4}c^{12}d^{-20}}{\left(2c^{2}\right)^{4}\times 16}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{c^{8}d^{-2}\times 16c^{12}d^{-20}}{\left(2c^{2}\right)^{4}\times 16}$$

To multiply powers of the same base, add their exponents. Add 8 and 12 to get 20.

$$\frac{c^{20}d^{-2}\times 16d^{-20}}{\left(2c^{2}\right)^{4}\times 16}$$

To multiply powers of the same base, add their exponents. Add -2 and -20 to get -22.

$$\frac{c^{20}d^{-22}\times 16}{\left(2c^{2}\right)^{4}\times 16}$$

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

$$\frac{c^{20}d^{-22}\times 16}{2^{4}\left(c^{2}\right)^{4}\times 16}$$

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

$$\frac{c^{20}d^{-22}\times 16}{2^{4}c^{8}\times 16}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{c^{20}d^{-22}\times 16}{16c^{8}\times 16}$$

Multiply 16 and 16 to get 256.

$$\frac{c^{20}d^{-22}\times 16}{256c^{8}}$$

Cancel out 16c^{8} in both numerator and denominator.

$$\frac{d^{-22}c^{12}}{16}$$