Solve (frac{a^{2}b}{-cd^3})^3div2a/d^5*(c/2a)^3

$$( \frac { a ^ { 2 } b } { - c d ^ { 3 } } ) ^ { 3 } \div \frac { 2 a } { d ^ { 5 } } \cdot ( \frac { c } { 2 a } ) ^ { 3 }$$

Evaluate

$$-\frac{a^{2}b^{3}}{16d^{4}}$$

Short Solution Steps

To raise \frac{a^{2}b}{\left(-c\right)d^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{a^{6}b^{3}d^{5}}{\left(-c\right)^{3}d^{9}\times 2a}\times \left(\frac{c}{2a}\right)^{3}$$

Cancel out ad^{5} in both numerator and denominator.

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

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

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

Multiply \frac{b^{3}a^{5}}{2\left(-c\right)^{3}d^{4}} times \frac{c^{3}}{\left(2a\right)^{3}} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Calculate 2 to the power of 3 and get 8.

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

Multiply 2 and 8 to get 16.

$$\frac{b^{3}a^{5}c^{3}}{16\left(-c\right)^{3}d^{4}a^{3}}$$

Cancel out a^{3} in both numerator and denominator.

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

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

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

Calculate -1 to the power of 3 and get -1.

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

Multiply 16 and -1 to get -16.

$$\frac{a^{2}b^{3}c^{3}}{-16c^{3}d^{4}}$$

Cancel out c^{3} in both numerator and denominator.

$$\frac{a^{2}b^{3}}{-16d^{4}}$$

Expand

$$-\frac{a^{2}b^{3}}{16d^{4}}$$

Short Solution Steps

To raise \frac{a^{2}b}{\left(-c\right)d^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{a^{6}b^{3}d^{5}}{\left(-c\right)^{3}d^{9}\times 2a}\times \left(\frac{c}{2a}\right)^{3}$$

Cancel out ad^{5} in both numerator and denominator.

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

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

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

Multiply \frac{b^{3}a^{5}}{2\left(-c\right)^{3}d^{4}} times \frac{c^{3}}{\left(2a\right)^{3}} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Calculate 2 to the power of 3 and get 8.

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

Multiply 2 and 8 to get 16.

$$\frac{b^{3}a^{5}c^{3}}{16\left(-c\right)^{3}d^{4}a^{3}}$$

Cancel out a^{3} in both numerator and denominator.

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

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

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

Calculate -1 to the power of 3 and get -1.

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

Multiply 16 and -1 to get -16.

$$\frac{a^{2}b^{3}c^{3}}{-16c^{3}d^{4}}$$

Cancel out c^{3} in both numerator and denominator.

$$\frac{a^{2}b^{3}}{-16d^{4}}$$