Solve (2a^3/bc^2)^3=

$$( \frac { 2 a ^ { 3 } } { b c ^ { 2 } } ) ^ { 3 } =$$

Evaluate

$$\frac{8a^{9}}{b^{3}c^{6}}$$

Solution Steps

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

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

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

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

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

$$\frac{2^{3}a^{9}}{\left(bc^{2}\right)^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8a^{9}}{\left(bc^{2}\right)^{3}}$$

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

$$\frac{8a^{9}}{b^{3}\left(c^{2}\right)^{3}}$$

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

$$\frac{8a^{9}}{b^{3}c^{6}}$$

Expand

$$\frac{8a^{9}}{b^{3}c^{6}}$$

Solution Steps

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

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

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

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

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

$$\frac{2^{3}a^{9}}{\left(bc^{2}\right)^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8a^{9}}{\left(bc^{2}\right)^{3}}$$

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

$$\frac{8a^{9}}{b^{3}\left(c^{2}\right)^{3}}$$

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

$$\frac{8a^{9}}{b^{3}c^{6}}$$