Solve (3a^2/4a^5b^2)^3

$$( \frac { 3 a ^ { 2 } } { 4 a ^ { 5 } b ^ { 2 } } ) ^ { 3 }$$

Evaluate

$$\frac{27}{64b^{6}a^{9}}$$

Solution Steps

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

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

To raise \frac{3}{4b^{2}a^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 3 to the power of 3 and get 27.

$$\frac{27}{\left(4b^{2}a^{3}\right)^{3}}$$

Expand \left(4b^{2}a^{3}\right)^{3}.

$$\frac{27}{4^{3}\left(b^{2}\right)^{3}\left(a^{3}\right)^{3}}$$

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

$$\frac{27}{4^{3}b^{6}\left(a^{3}\right)^{3}}$$

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

$$\frac{27}{4^{3}b^{6}a^{9}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{27}{64b^{6}a^{9}}$$

Expand

$$\frac{27}{64b^{6}a^{9}}$$

Solution Steps

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

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

To raise \frac{3}{4b^{2}a^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 3 to the power of 3 and get 27.

$$\frac{27}{\left(4b^{2}a^{3}\right)^{3}}$$

Expand \left(4b^{2}a^{3}\right)^{3}.

$$\frac{27}{4^{3}\left(b^{2}\right)^{3}\left(a^{3}\right)^{3}}$$

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

$$\frac{27}{4^{3}b^{6}\left(a^{3}\right)^{3}}$$

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

$$\frac{27}{4^{3}b^{6}a^{9}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{27}{64b^{6}a^{9}}$$