Solve -2(a^{3})^{2}-(a^{2})^{3}-(-a)^{6}+(2a^2+8a^2)^2:a^4

$$- 2 ( a ^ { 3 } ) ^ { 2 } - ( a ^ { 2 } ) ^ { 3 } - ( - a ) ^ { 6 } + ( 2 a ^ { 2 } + 8 a ^ { 2 } ) ^ { 2 } : a ^ { 4 }$$

Evaluate

$$100-4a^{6}$$

Solution Steps

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

$$-2a^{6}-\left(a^{2}\right)^{3}-\left(-a\right)^{6}+\frac{\left(2a^{2}+8a^{2}\right)^{2}}{a^{4}}$$

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

$$-2a^{6}-a^{6}-\left(-a\right)^{6}+\frac{\left(2a^{2}+8a^{2}\right)^{2}}{a^{4}}$$

Combine -2a^{6} and -a^{6} to get -3a^{6}.

$$-3a^{6}-\left(-a\right)^{6}+\frac{\left(2a^{2}+8a^{2}\right)^{2}}{a^{4}}$$

Combine 2a^{2} and 8a^{2} to get 10a^{2}.

$$-3a^{6}-\left(-a\right)^{6}+\frac{\left(10a^{2}\right)^{2}}{a^{4}}$$

Expand \left(10a^{2}\right)^{2}.

$$-3a^{6}-\left(-a\right)^{6}+\frac{10^{2}\left(a^{2}\right)^{2}}{a^{4}}$$

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

$$-3a^{6}-\left(-a\right)^{6}+\frac{10^{2}a^{4}}{a^{4}}$$

Calculate 10 to the power of 2 and get 100.

$$-3a^{6}-\left(-a\right)^{6}+\frac{100a^{4}}{a^{4}}$$

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

$$-3a^{6}-\left(-a\right)^{6}+100$$

Expand \left(-a\right)^{6}.

$$-3a^{6}-\left(-1\right)^{6}a^{6}+100$$

Calculate -1 to the power of 6 and get 1.

$$-3a^{6}-a^{6}+100$$

Combine -3a^{6} and -a^{6} to get -4a^{6}.

$$-4a^{6}+100$$

Expand

$$100-4a^{6}$$

Solution Steps

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

$$-2a^{6}-\left(a^{2}\right)^{3}-\left(-a\right)^{6}+\frac{\left(2a^{2}+8a^{2}\right)^{2}}{a^{4}}$$

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

$$-2a^{6}-a^{6}-\left(-a\right)^{6}+\frac{\left(2a^{2}+8a^{2}\right)^{2}}{a^{4}}$$

Combine -2a^{6} and -a^{6} to get -3a^{6}.

$$-3a^{6}-\left(-a\right)^{6}+\frac{\left(2a^{2}+8a^{2}\right)^{2}}{a^{4}}$$

Combine 2a^{2} and 8a^{2} to get 10a^{2}.

$$-3a^{6}-\left(-a\right)^{6}+\frac{\left(10a^{2}\right)^{2}}{a^{4}}$$

Expand \left(10a^{2}\right)^{2}.

$$-3a^{6}-\left(-a\right)^{6}+\frac{10^{2}\left(a^{2}\right)^{2}}{a^{4}}$$

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

$$-3a^{6}-\left(-a\right)^{6}+\frac{10^{2}a^{4}}{a^{4}}$$

Calculate 10 to the power of 2 and get 100.

$$-3a^{6}-\left(-a\right)^{6}+\frac{100a^{4}}{a^{4}}$$

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

$$-3a^{6}-\left(-a\right)^{6}+100$$

Expand \left(-a\right)^{6}.

$$-3a^{6}-\left(-1\right)^{6}a^{6}+100$$

Calculate -1 to the power of 6 and get 1.

$$-3a^{6}-a^{6}+100$$

Combine -3a^{6} and -a^{6} to get -4a^{6}.

$$-4a^{6}+100$$