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

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

Evaluate

$$\frac{8a^{15}}{27b^{12}}$$

Solution Steps

To raise \frac{2a^{5}}{3b^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(2a^{5}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{2^{3}a^{15}}{\left(3b^{4}\right)^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8a^{15}}{\left(3b^{4}\right)^{3}}$$

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

$$\frac{8a^{15}}{3^{3}\left(b^{4}\right)^{3}}$$

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

$$\frac{8a^{15}}{3^{3}b^{12}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{8a^{15}}{27b^{12}}$$

Expand

$$\frac{8a^{15}}{27b^{12}}$$

Solution Steps

To raise \frac{2a^{5}}{3b^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(2a^{5}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{2^{3}a^{15}}{\left(3b^{4}\right)^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8a^{15}}{\left(3b^{4}\right)^{3}}$$

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

$$\frac{8a^{15}}{3^{3}\left(b^{4}\right)^{3}}$$

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

$$\frac{8a^{15}}{3^{3}b^{12}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{8a^{15}}{27b^{12}}$$