Solve (a^2b/-cd^3)^3div2a/d^3*(c/2a)

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

Evaluate

$$-\frac{b^{3}a^{4}}{4c^{2}d^{6}}$$

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Cancel out a in both numerator and denominator.

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

Multiply 2 and 2 to get 4.

$$\frac{cb^{3}a^{4}}{4\left(-c\right)^{3}d^{6}}$$

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

$$\frac{cb^{3}a^{4}}{4\left(-1\right)^{3}c^{3}d^{6}}$$

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

$$\frac{cb^{3}a^{4}}{4\left(-1\right)c^{3}d^{6}}$$

Multiply 4 and -1 to get -4.

$$\frac{cb^{3}a^{4}}{-4c^{3}d^{6}}$$

Cancel out c in both numerator and denominator.

$$\frac{b^{3}a^{4}}{-4c^{2}d^{6}}$$

Expand

$$-\frac{b^{3}a^{4}}{4c^{2}d^{6}}$$

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Cancel out a in both numerator and denominator.

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

Multiply 2 and 2 to get 4.

$$\frac{cb^{3}a^{4}}{4\left(-c\right)^{3}d^{6}}$$

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

$$\frac{cb^{3}a^{4}}{4\left(-1\right)^{3}c^{3}d^{6}}$$

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

$$\frac{cb^{3}a^{4}}{4\left(-1\right)c^{3}d^{6}}$$

Multiply 4 and -1 to get -4.

$$\frac{cb^{3}a^{4}}{-4c^{3}d^{6}}$$

Cancel out c in both numerator and denominator.

$$\frac{b^{3}a^{4}}{-4c^{2}d^{6}}$$