Solve x^{5}-x^7+x^6*(-x^3)^2

$$x ^ { 5 } - x ^ { 7 } + x ^ { 6 } \cdot ( - x ^ { 3 } ) ^ { 2 }$$

Evaluate

$$x^{12}-x^{7}+x^{5}$$

Solution Steps

Calculate -x^{3} to the power of 2 and get \left(x^{3}\right)^{2}.

$$x^{5}-x^{7}+x^{6}\left(x^{3}\right)^{2}$$

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

$$x^{5}-x^{7}+x^{6}x^{6}$$

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

$$x^{5}-x^{7}+x^{12}$$

Expand

$$x^{12}-x^{7}+x^{5}$$

Solution Steps

Calculate -x^{3} to the power of 2 and get \left(x^{3}\right)^{2}.

$$x^{5}-x^{7}+x^{6}\left(x^{3}\right)^{2}$$

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

$$x^{5}-x^{7}+x^{6}x^{6}$$

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

$$x^{5}-x^{7}+x^{12}$$