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

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

Evaluate

$$\frac{1}{b^{2}a^{3}}$$

Solution Steps

To raise \frac{a^{3}}{b^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

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

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

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

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

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

$$\frac{b^{6}}{a^{3}b^{8}}$$

Cancel out b^{6} in both numerator and denominator.

$$\frac{1}{b^{2}a^{3}}$$

Expand

$$\frac{1}{b^{2}a^{3}}$$

Solution Steps

To raise \frac{a^{3}}{b^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

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

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

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

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

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

$$\frac{b^{6}}{a^{3}b^{8}}$$

Cancel out b^{6} in both numerator and denominator.

$$\frac{1}{b^{2}a^{3}}$$