Solve (4a^4/3a^6b^3)^3

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

Evaluate

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

Solution Steps

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

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

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

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

Calculate 4 to the power of 3 and get 64.

$$\frac{64}{\left(3a^{2}b^{3}\right)^{3}}$$

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

$$\frac{64}{3^{3}\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}}$$

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

$$\frac{64}{3^{3}a^{6}\left(b^{3}\right)^{3}}$$

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

$$\frac{64}{3^{3}a^{6}b^{9}}$$

Calculate 3 to the power of 3 and get 27.

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

Expand

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

Solution Steps

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

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

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

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

Calculate 4 to the power of 3 and get 64.

$$\frac{64}{\left(3a^{2}b^{3}\right)^{3}}$$

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

$$\frac{64}{3^{3}\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}}$$

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

$$\frac{64}{3^{3}a^{6}\left(b^{3}\right)^{3}}$$

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

$$\frac{64}{3^{3}a^{6}b^{9}}$$

Calculate 3 to the power of 3 and get 27.

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