Solve (2a^{3})^{4}:(-8a^{7})+3(-a)^5]^2-(-2a^5)^2

$$( 2 a ^ { 3 } ) ^ { 4 } : ( - 8 a ^ { 7 } ) + 3 ( - a ) ^ { 5 } ] ^ { 2 } - ( - 2 a ^ { 5 } ) ^ { 2 }$$

Evaluate

$$-5a^{5}$$

Solution Steps

Expand \left(2a^{3}\right)^{4}.

$$\frac{2^{4}\left(a^{3}\right)^{4}}{-8a^{7}}+3\left(-a\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{2^{4}a^{12}}{-8a^{7}}+3\left(-a\right)^{5}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16a^{12}}{-8a^{7}}+3\left(-a\right)^{5}$$

Cancel out 8a^{7} in both numerator and denominator.

$$\frac{2a^{5}}{-1}+3\left(-a\right)^{5}$$

Anything divided by -1 gives its opposite.

$$-2a^{5}+3\left(-a\right)^{5}$$

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

$$-2a^{5}+3\left(-1\right)^{5}a^{5}$$

Calculate -1 to the power of 5 and get -1.

$$-2a^{5}+3\left(-1\right)a^{5}$$

Multiply 3 and -1 to get -3.

$$-2a^{5}-3a^{5}$$

Combine -2a^{5} and -3a^{5} to get -5a^{5}.

$$-5a^{5}$$

Expand

$$-5a^{5}$$

Solution Steps

Expand \left(2a^{3}\right)^{4}.

$$\frac{2^{4}\left(a^{3}\right)^{4}}{-8a^{7}}+3\left(-a\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{2^{4}a^{12}}{-8a^{7}}+3\left(-a\right)^{5}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16a^{12}}{-8a^{7}}+3\left(-a\right)^{5}$$

Cancel out 8a^{7} in both numerator and denominator.

$$\frac{2a^{5}}{-1}+3\left(-a\right)^{5}$$

Anything divided by -1 gives its opposite.

$$-2a^{5}+3\left(-a\right)^{5}$$

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

$$-2a^{5}+3\left(-1\right)^{5}a^{5}$$

Calculate -1 to the power of 5 and get -1.

$$-2a^{5}+3\left(-1\right)a^{5}$$

Multiply 3 and -1 to get -3.

$$-2a^{5}-3a^{5}$$

Combine -2a^{5} and -3a^{5} to get -5a^{5}.

$$-5a^{5}$$