Solve frac{(a^{2}bc^3)^2}{d^2}:(ab/b)^4

$$\frac { ( a ^ { 2 } b c ^ { 3 } ) ^ { 2 } } { d ^ { 2 } } : ( \frac { a b } { b } ) ^ { 4 }$$

Evaluate

$$\left(\frac{b}{d}\right)^{2}c^{6}$$

Solution Steps

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

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

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

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

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

$$\frac{\frac{a^{4}b^{2}c^{6}}{d^{2}}}{\left(\frac{ab}{b}\right)^{4}}$$

Cancel out b in both numerator and denominator.

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

Express \frac{\frac{a^{4}b^{2}c^{6}}{d^{2}}}{a^{4}} as a single fraction.

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

Cancel out a^{4} in both numerator and denominator.

$$\frac{b^{2}c^{6}}{d^{2}}$$

Expand

$$\left(\frac{b}{d}\right)^{2}c^{6}$$

Solution Steps

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

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

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

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

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

$$\frac{\frac{a^{4}b^{2}c^{6}}{d^{2}}}{\left(\frac{ab}{b}\right)^{4}}$$

Cancel out b in both numerator and denominator.

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

Express \frac{\frac{a^{4}b^{2}c^{6}}{d^{2}}}{a^{4}} as a single fraction.

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

Cancel out a^{4} in both numerator and denominator.

$$\frac{b^{2}c^{6}}{d^{2}}$$