Solve 2*(a^4b^-2/c^3)^2=

$$2 \cdot ( \frac { a ^ { 4 } b ^ { - 2 } } { c ^ { 3 } } ) ^ { 2 } =$$

Evaluate

$$\frac{2a^{8}}{b^{4}c^{6}}$$

Solution Steps

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

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

Express 2\times \frac{\left(a^{4}b^{-2}\right)^{2}}{\left(c^{3}\right)^{2}} as a single fraction.

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

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

$$\frac{2\left(a^{4}b^{-2}\right)^{2}}{c^{6}}$$

Expand \left(a^{4}b^{-2}\right)^{2}.

$$\frac{2\left(a^{4}\right)^{2}\left(b^{-2}\right)^{2}}{c^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{2a^{8}\left(b^{-2}\right)^{2}}{c^{6}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 2 to get -4.

$$\frac{2a^{8}b^{-4}}{c^{6}}$$

Expand

$$\frac{2a^{8}}{b^{4}c^{6}}$$

Solution Steps

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

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

Express 2\times \frac{\left(a^{4}b^{-2}\right)^{2}}{\left(c^{3}\right)^{2}} as a single fraction.

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

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

$$\frac{2\left(a^{4}b^{-2}\right)^{2}}{c^{6}}$$

Expand \left(a^{4}b^{-2}\right)^{2}.

$$\frac{2\left(a^{4}\right)^{2}\left(b^{-2}\right)^{2}}{c^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{2a^{8}\left(b^{-2}\right)^{2}}{c^{6}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 2 to get -4.

$$\frac{2a^{8}b^{-4}}{c^{6}}$$