Solve frac{a^{3}b}{2c}divab^2/c^2*(-2b^2/ac)^2

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

Evaluate

$$\frac{2b^{3}}{c}$$

Solution Steps

Divide \frac{a^{3}b}{2c} by \frac{ab^{2}}{c^{2}} by multiplying \frac{a^{3}b}{2c} by the reciprocal of \frac{ab^{2}}{c^{2}}.

$$\frac{a^{3}bc^{2}}{2cab^{2}}\times \left(\frac{-2b^{2}}{ac}\right)^{2}$$

Cancel out abc in both numerator and denominator.

$$\frac{ca^{2}}{2b}\times \left(\frac{-2b^{2}}{ac}\right)^{2}$$

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

$$\frac{ca^{2}}{2b}\times \frac{\left(-2b^{2}\right)^{2}}{\left(ac\right)^{2}}$$

Multiply \frac{ca^{2}}{2b} times \frac{\left(-2b^{2}\right)^{2}}{\left(ac\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{ca^{2}\left(-2b^{2}\right)^{2}}{2b\left(ac\right)^{2}}$$

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

$$\frac{ca^{2}\left(-2\right)^{2}\left(b^{2}\right)^{2}}{2b\left(ac\right)^{2}}$$

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

$$\frac{ca^{2}\left(-2\right)^{2}b^{4}}{2b\left(ac\right)^{2}}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{ca^{2}\times 4b^{4}}{2b\left(ac\right)^{2}}$$

Expand \left(ac\right)^{2}.

$$\frac{ca^{2}\times 4b^{4}}{2ba^{2}c^{2}}$$

Cancel out 2bca^{2} in both numerator and denominator.

$$\frac{2b^{3}}{c}$$

Expand

$$\frac{2b^{3}}{c}$$

Solution Steps

Divide \frac{a^{3}b}{2c} by \frac{ab^{2}}{c^{2}} by multiplying \frac{a^{3}b}{2c} by the reciprocal of \frac{ab^{2}}{c^{2}}.

$$\frac{a^{3}bc^{2}}{2cab^{2}}\times \left(\frac{-2b^{2}}{ac}\right)^{2}$$

Cancel out abc in both numerator and denominator.

$$\frac{ca^{2}}{2b}\times \left(\frac{-2b^{2}}{ac}\right)^{2}$$

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

$$\frac{ca^{2}}{2b}\times \frac{\left(-2b^{2}\right)^{2}}{\left(ac\right)^{2}}$$

Multiply \frac{ca^{2}}{2b} times \frac{\left(-2b^{2}\right)^{2}}{\left(ac\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{ca^{2}\left(-2b^{2}\right)^{2}}{2b\left(ac\right)^{2}}$$

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

$$\frac{ca^{2}\left(-2\right)^{2}\left(b^{2}\right)^{2}}{2b\left(ac\right)^{2}}$$

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

$$\frac{ca^{2}\left(-2\right)^{2}b^{4}}{2b\left(ac\right)^{2}}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{ca^{2}\times 4b^{4}}{2b\left(ac\right)^{2}}$$

Expand \left(ac\right)^{2}.

$$\frac{ca^{2}\times 4b^{4}}{2ba^{2}c^{2}}$$

Cancel out 2bca^{2} in both numerator and denominator.

$$\frac{2b^{3}}{c}$$