Solve =(frac{a*b^{2}}{c^{2}*d^{3}})^{4}*(c^6*d^4/a*b^2)^2

$$= ( \frac { a \cdot b ^ { 2 } } { c ^ { 2 } \cdot d ^ { 3 } } ) ^ { 4 } \times ( \frac { c ^ { 6 } \cdot d ^ { 4 } } { a \cdot b ^ { 2 } } ) ^ { 2 }$$

Evaluate

$$a^{2}\times \left(\frac{bc}{d}\right)^{4}$$

Solution Steps

To raise \frac{ab^{2}}{c^{2}d^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise \frac{c^{6}d^{4}}{ab^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

Multiply \frac{\left(ab^{2}\right)^{4}}{\left(c^{2}d^{3}\right)^{4}} times \frac{\left(c^{6}d^{4}\right)^{2}}{\left(ab^{2}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(ab^{2}\right)^{4}\left(c^{6}d^{4}\right)^{2}}{\left(c^{2}d^{3}\right)^{4}\left(ab^{2}\right)^{2}}$$

Cancel out \left(ab^{2}\right)^{2} in both numerator and denominator.

$$\frac{\left(ab^{2}\right)^{2}\left(d^{4}c^{6}\right)^{2}}{\left(c^{2}d^{3}\right)^{4}}$$

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

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

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

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

Expand \left(d^{4}c^{6}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{a^{2}b^{4}d^{8}\left(c^{6}\right)^{2}}{\left(c^{2}d^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{a^{2}b^{4}d^{8}c^{12}}{\left(c^{2}d^{3}\right)^{4}}$$

Expand \left(c^{2}d^{3}\right)^{4}.

$$\frac{a^{2}b^{4}d^{8}c^{12}}{\left(c^{2}\right)^{4}\left(d^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{a^{2}b^{4}d^{8}c^{12}}{c^{8}\left(d^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{a^{2}b^{4}d^{8}c^{12}}{c^{8}d^{12}}$$

Cancel out c^{8}d^{8} in both numerator and denominator.

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

Expand

$$a^{2}\times \left(\frac{bc}{d}\right)^{4}$$

Solution Steps

To raise \frac{ab^{2}}{c^{2}d^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise \frac{c^{6}d^{4}}{ab^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

Multiply \frac{\left(ab^{2}\right)^{4}}{\left(c^{2}d^{3}\right)^{4}} times \frac{\left(c^{6}d^{4}\right)^{2}}{\left(ab^{2}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(ab^{2}\right)^{4}\left(c^{6}d^{4}\right)^{2}}{\left(c^{2}d^{3}\right)^{4}\left(ab^{2}\right)^{2}}$$

Cancel out \left(ab^{2}\right)^{2} in both numerator and denominator.

$$\frac{\left(ab^{2}\right)^{2}\left(d^{4}c^{6}\right)^{2}}{\left(c^{2}d^{3}\right)^{4}}$$

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

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

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

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

Expand \left(d^{4}c^{6}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{a^{2}b^{4}d^{8}\left(c^{6}\right)^{2}}{\left(c^{2}d^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{a^{2}b^{4}d^{8}c^{12}}{\left(c^{2}d^{3}\right)^{4}}$$

Expand \left(c^{2}d^{3}\right)^{4}.

$$\frac{a^{2}b^{4}d^{8}c^{12}}{\left(c^{2}\right)^{4}\left(d^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{a^{2}b^{4}d^{8}c^{12}}{c^{8}\left(d^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{a^{2}b^{4}d^{8}c^{12}}{c^{8}d^{12}}$$

Cancel out c^{8}d^{8} in both numerator and denominator.

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