Solve (2a^4b^5/6b^2)^3

$$( \frac { 2 a ^ { 4 } b ^ { 5 } } { 6 b ^ { 2 } } ) ^ { 3 }$$

Evaluate

$$\frac{b^{9}a^{12}}{27}$$

Solution Steps

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

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

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

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

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

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

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

$$\frac{b^{9}\left(a^{4}\right)^{3}}{3^{3}}$$

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

$$\frac{b^{9}a^{12}}{3^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{b^{9}a^{12}}{27}$$

Expand

$$\frac{b^{9}a^{12}}{27}$$

Solution Steps

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

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

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

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

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

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

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

$$\frac{b^{9}\left(a^{4}\right)^{3}}{3^{3}}$$

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

$$\frac{b^{9}a^{12}}{3^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{b^{9}a^{12}}{27}$$