Solve (1)[(-a^{5})^4diva^12]^2*(-2a^4)

$$( 1 ) [ ( - a ^ { 5 } ) ^ { 4 } \div a ^ { 12 } ] ^ { 2 } \cdot ( - 2 a ^ { 4 } )$$

Evaluate

$$-2a^{20}$$

Short Solution Steps

To raise \frac{\left(-a^{5}\right)^{4}}{a^{12}} to a power, raise both numerator and denominator to the power and then divide.

$$1\times \frac{\left(\left(-a^{5}\right)^{4}\right)^{2}}{\left(a^{12}\right)^{2}}\left(-2\right)a^{4}$$

Multiply 1 and -2 to get -2.

$$-2\times \frac{\left(\left(-a^{5}\right)^{4}\right)^{2}}{\left(a^{12}\right)^{2}}a^{4}$$

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

$$-2\times \frac{\left(-a^{5}\right)^{8}}{\left(a^{12}\right)^{2}}a^{4}$$

To raise a power to another power, multiply the exponents. Multiply 12 and 2 to get 24.

$$-2\times \frac{\left(-a^{5}\right)^{8}}{a^{24}}a^{4}$$

Express -2\times \frac{\left(-a^{5}\right)^{8}}{a^{24}} as a single fraction.

$$\frac{-2\left(-a^{5}\right)^{8}}{a^{24}}a^{4}$$

Express \frac{-2\left(-a^{5}\right)^{8}}{a^{24}}a^{4} as a single fraction.

$$\frac{-2\left(-a^{5}\right)^{8}a^{4}}{a^{24}}$$

Cancel out a^{4} in both numerator and denominator.

$$\frac{-2\left(-a^{5}\right)^{8}}{a^{20}}$$

Expand \left(-a^{5}\right)^{8}.

$$\frac{-2\left(-1\right)^{8}\left(a^{5}\right)^{8}}{a^{20}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 8 to get 40.

$$\frac{-2\left(-1\right)^{8}a^{40}}{a^{20}}$$

Calculate -1 to the power of 8 and get 1.

$$\frac{-2a^{40}}{a^{20}}$$

Cancel out a^{20} in both numerator and denominator.

$$-2a^{20}$$

Expand

$$-2a^{20}$$

Short Solution Steps

To raise \frac{\left(-a^{5}\right)^{4}}{a^{12}} to a power, raise both numerator and denominator to the power and then divide.

$$1\times \frac{\left(\left(-a^{5}\right)^{4}\right)^{2}}{\left(a^{12}\right)^{2}}\left(-2\right)a^{4}$$

Multiply 1 and -2 to get -2.

$$-2\times \frac{\left(\left(-a^{5}\right)^{4}\right)^{2}}{\left(a^{12}\right)^{2}}a^{4}$$

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

$$-2\times \frac{\left(-a^{5}\right)^{8}}{\left(a^{12}\right)^{2}}a^{4}$$

To raise a power to another power, multiply the exponents. Multiply 12 and 2 to get 24.

$$-2\times \frac{\left(-a^{5}\right)^{8}}{a^{24}}a^{4}$$

Express -2\times \frac{\left(-a^{5}\right)^{8}}{a^{24}} as a single fraction.

$$\frac{-2\left(-a^{5}\right)^{8}}{a^{24}}a^{4}$$

Express \frac{-2\left(-a^{5}\right)^{8}}{a^{24}}a^{4} as a single fraction.

$$\frac{-2\left(-a^{5}\right)^{8}a^{4}}{a^{24}}$$

Cancel out a^{4} in both numerator and denominator.

$$\frac{-2\left(-a^{5}\right)^{8}}{a^{20}}$$

Expand \left(-a^{5}\right)^{8}.

$$\frac{-2\left(-1\right)^{8}\left(a^{5}\right)^{8}}{a^{20}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 8 to get 40.

$$\frac{-2\left(-1\right)^{8}a^{40}}{a^{20}}$$

Calculate -1 to the power of 8 and get 1.

$$\frac{-2a^{40}}{a^{20}}$$

Cancel out a^{20} in both numerator and denominator.

$$-2a^{20}$$