Solve 14(b^3/a^2)^5

$$14 ( \frac { b ^ { 3 } } { a ^ { 2 } } ) ^ { 5 }$$

Evaluate

$$\frac{14b^{15}}{a^{10}}$$

Solution Steps

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

$$14\times \frac{\left(b^{3}\right)^{5}}{\left(a^{2}\right)^{5}}$$

Express 14\times \frac{\left(b^{3}\right)^{5}}{\left(a^{2}\right)^{5}} as a single fraction.

$$\frac{14\left(b^{3}\right)^{5}}{\left(a^{2}\right)^{5}}$$

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

$$\frac{14b^{15}}{\left(a^{2}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{14b^{15}}{a^{10}}$$

Expand

$$\frac{14b^{15}}{a^{10}}$$

Solution Steps

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

$$14\times \frac{\left(b^{3}\right)^{5}}{\left(a^{2}\right)^{5}}$$

Express 14\times \frac{\left(b^{3}\right)^{5}}{\left(a^{2}\right)^{5}} as a single fraction.

$$\frac{14\left(b^{3}\right)^{5}}{\left(a^{2}\right)^{5}}$$

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

$$\frac{14b^{15}}{\left(a^{2}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{14b^{15}}{a^{10}}$$