Solve a^{6}*(-a^{2})^3+a^2*(-a^5)^2

$$a ^ { 6 } \cdot ( - a ^ { 2 } ) ^ { 3 } + a ^ { 2 } \cdot ( - a ^ { 5 } ) ^ { 2 }$$

Evaluate

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Solution Steps

Calculate -a^{5} to the power of 2 and get \left(a^{5}\right)^{2}.

$$a^{6}\left(-a^{2}\right)^{3}+a^{2}\left(a^{5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

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

To multiply powers of the same base, add their exponents. Add 2 and 10 to get 12.

$$a^{6}\left(-a^{2}\right)^{3}+a^{12}$$

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

$$a^{6}\left(-1\right)^{3}\left(a^{2}\right)^{3}+a^{12}$$

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

$$a^{6}\left(-1\right)^{3}a^{6}+a^{12}$$

Calculate -1 to the power of 3 and get -1.

$$a^{6}\left(-1\right)a^{6}+a^{12}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$a^{12}\left(-1\right)+a^{12}$$

Combine a^{12}\left(-1\right) and a^{12} to get 0.

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Factor

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Solution Steps

Factor out common term a^{2} by using distributive property.

$$a^{2}\left(-a^{10}+\left(-a^{5}\right)^{2}\right)$$

Consider -a^{10}+\left(-a^{5}\right)^{2}. Simplify.

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