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

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

Evaluate

$$-\frac{108d^{7}}{c^{33}}$$

Solution Steps

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

$$\left(\frac{2cd^{6}}{-3}\right)^{-3}\times \left(\frac{2c^{-4}d^{2}}{c^{2}d^{-3}}\right)^{5}$$

To raise \frac{2cd^{6}}{-3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2cd^{6}\right)^{-3}}{\left(-3\right)^{-3}}\times \left(\frac{2c^{-4}d^{2}}{c^{2}d^{-3}}\right)^{5}$$

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

$$\frac{\left(2cd^{6}\right)^{-3}}{\left(-3\right)^{-3}}\times \left(\frac{2c^{-4}d^{5}}{c^{2}}\right)^{5}$$

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

$$\frac{\left(2cd^{6}\right)^{-3}}{\left(-3\right)^{-3}}\times \left(\frac{2d^{5}}{c^{6}}\right)^{5}$$

To raise \frac{2d^{5}}{c^{6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2cd^{6}\right)^{-3}}{\left(-3\right)^{-3}}\times \frac{\left(2d^{5}\right)^{5}}{\left(c^{6}\right)^{5}}$$

Multiply \frac{\left(2cd^{6}\right)^{-3}}{\left(-3\right)^{-3}} times \frac{\left(2d^{5}\right)^{5}}{\left(c^{6}\right)^{5}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2cd^{6}\right)^{-3}\times \left(2d^{5}\right)^{5}}{\left(-3\right)^{-3}\left(c^{6}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 5 to get 30.

$$\frac{\left(2cd^{6}\right)^{-3}\times \left(2d^{5}\right)^{5}}{\left(-3\right)^{-3}c^{30}}$$

Expand \left(2cd^{6}\right)^{-3}.

$$\frac{2^{-3}c^{-3}\left(d^{6}\right)^{-3}\times \left(2d^{5}\right)^{5}}{\left(-3\right)^{-3}c^{30}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -3 to get -18.

$$\frac{2^{-3}c^{-3}d^{-18}\times \left(2d^{5}\right)^{5}}{\left(-3\right)^{-3}c^{30}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{\frac{1}{8}c^{-3}d^{-18}\times \left(2d^{5}\right)^{5}}{\left(-3\right)^{-3}c^{30}}$$

Expand \left(2d^{5}\right)^{5}.

$$\frac{\frac{1}{8}c^{-3}d^{-18}\times 2^{5}\left(d^{5}\right)^{5}}{\left(-3\right)^{-3}c^{30}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 5 to get 25.

$$\frac{\frac{1}{8}c^{-3}d^{-18}\times 2^{5}d^{25}}{\left(-3\right)^{-3}c^{30}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{\frac{1}{8}c^{-3}d^{-18}\times 32d^{25}}{\left(-3\right)^{-3}c^{30}}$$

Multiply \frac{1}{8} and 32 to get 4.

$$\frac{4c^{-3}d^{-18}d^{25}}{\left(-3\right)^{-3}c^{30}}$$

To multiply powers of the same base, add their exponents. Add -18 and 25 to get 7.

$$\frac{4c^{-3}d^{7}}{\left(-3\right)^{-3}c^{30}}$$

Calculate -3 to the power of -3 and get -\frac{1}{27}.

$$\frac{4c^{-3}d^{7}}{-\frac{1}{27}c^{30}}$$

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

$$\frac{4d^{7}}{-\frac{1}{27}c^{33}}$$

Expand

$$-\frac{108d^{7}}{c^{33}}$$

Solution Steps

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

$$\left(\frac{2cd^{6}}{-3}\right)^{-3}\times \left(\frac{2c^{-4}d^{2}}{c^{2}d^{-3}}\right)^{5}$$

To raise \frac{2cd^{6}}{-3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2cd^{6}\right)^{-3}}{\left(-3\right)^{-3}}\times \left(\frac{2c^{-4}d^{2}}{c^{2}d^{-3}}\right)^{5}$$

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

$$\frac{\left(2cd^{6}\right)^{-3}}{\left(-3\right)^{-3}}\times \left(\frac{2c^{-4}d^{5}}{c^{2}}\right)^{5}$$

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

$$\frac{\left(2cd^{6}\right)^{-3}}{\left(-3\right)^{-3}}\times \left(\frac{2d^{5}}{c^{6}}\right)^{5}$$

To raise \frac{2d^{5}}{c^{6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2cd^{6}\right)^{-3}}{\left(-3\right)^{-3}}\times \frac{\left(2d^{5}\right)^{5}}{\left(c^{6}\right)^{5}}$$

Multiply \frac{\left(2cd^{6}\right)^{-3}}{\left(-3\right)^{-3}} times \frac{\left(2d^{5}\right)^{5}}{\left(c^{6}\right)^{5}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2cd^{6}\right)^{-3}\times \left(2d^{5}\right)^{5}}{\left(-3\right)^{-3}\left(c^{6}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 5 to get 30.

$$\frac{\left(2cd^{6}\right)^{-3}\times \left(2d^{5}\right)^{5}}{\left(-3\right)^{-3}c^{30}}$$

Expand \left(2cd^{6}\right)^{-3}.

$$\frac{2^{-3}c^{-3}\left(d^{6}\right)^{-3}\times \left(2d^{5}\right)^{5}}{\left(-3\right)^{-3}c^{30}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -3 to get -18.

$$\frac{2^{-3}c^{-3}d^{-18}\times \left(2d^{5}\right)^{5}}{\left(-3\right)^{-3}c^{30}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{\frac{1}{8}c^{-3}d^{-18}\times \left(2d^{5}\right)^{5}}{\left(-3\right)^{-3}c^{30}}$$

Expand \left(2d^{5}\right)^{5}.

$$\frac{\frac{1}{8}c^{-3}d^{-18}\times 2^{5}\left(d^{5}\right)^{5}}{\left(-3\right)^{-3}c^{30}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 5 to get 25.

$$\frac{\frac{1}{8}c^{-3}d^{-18}\times 2^{5}d^{25}}{\left(-3\right)^{-3}c^{30}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{\frac{1}{8}c^{-3}d^{-18}\times 32d^{25}}{\left(-3\right)^{-3}c^{30}}$$

Multiply \frac{1}{8} and 32 to get 4.

$$\frac{4c^{-3}d^{-18}d^{25}}{\left(-3\right)^{-3}c^{30}}$$

To multiply powers of the same base, add their exponents. Add -18 and 25 to get 7.

$$\frac{4c^{-3}d^{7}}{\left(-3\right)^{-3}c^{30}}$$

Calculate -3 to the power of -3 and get -\frac{1}{27}.

$$\frac{4c^{-3}d^{7}}{-\frac{1}{27}c^{30}}$$

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

$$\frac{4d^{7}}{-\frac{1}{27}c^{33}}$$