Solve a^7*(-a^5)-(-a)^6*a^6

$$a ^ { 7 } \cdot ( - a ^ { 5 } ) - ( - a ) ^ { 6 } \cdot a ^ { 6 }$$

Evaluate

$$-2a^{12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 5 to get 12.

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

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

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

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

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

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 -2a^{12}.

$$-2a^{12}$$

Expand

$$-2a^{12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 5 to get 12.

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

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

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

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

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

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 -2a^{12}.

$$-2a^{12}$$