Solve (frac{a^{2}}{b})^4*(b^3/a^2)^3

$$( \frac { a ^ { 2 } } { b } ) ^ { 4 } \times ( \frac { b ^ { 3 } } { a ^ { 2 } } ) ^ { 3 }$$

Evaluate

$$a^{2}b^{5}$$

Solution Steps

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

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

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

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

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

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

Cancel out \left(a^{2}\right)^{3} in both numerator and denominator.

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

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

$$\frac{a^{2}b^{9}}{b^{4}}$$

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

$$a^{2}b^{5}$$

Expand

$$a^{2}b^{5}$$

Solution Steps

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

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

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

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

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

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

Cancel out \left(a^{2}\right)^{3} in both numerator and denominator.

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

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

$$\frac{a^{2}b^{9}}{b^{4}}$$

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

$$a^{2}b^{5}$$