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

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

Evaluate

$$a^{3}-a^{6}-4a^{9}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(-a^{2}\right)^{3}+a^{3}+\left(-a\right)^{2}a^{7}-5a^{9}$$

Calculate -a to the power of 2 and get a^{2}.

$$\left(-a^{2}\right)^{3}+a^{3}+a^{2}a^{7}-5a^{9}$$

To multiply powers of the same base, add their exponents. Add 2 and 7 to get 9.

$$\left(-a^{2}\right)^{3}+a^{3}+a^{9}-5a^{9}$$

Combine a^{9} and -5a^{9} to get -4a^{9}.

$$\left(-a^{2}\right)^{3}+a^{3}-4a^{9}$$

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

$$\left(-1\right)^{3}\left(a^{2}\right)^{3}+a^{3}-4a^{9}$$

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

$$\left(-1\right)^{3}a^{6}+a^{3}-4a^{9}$$

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

$$-a^{6}+a^{3}-4a^{9}$$

Expand

$$a^{3}-a^{6}-4a^{9}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(-a^{2}\right)^{3}+a^{3}+\left(-a\right)^{2}a^{7}-5a^{9}$$

Calculate -a to the power of 2 and get a^{2}.

$$\left(-a^{2}\right)^{3}+a^{3}+a^{2}a^{7}-5a^{9}$$

To multiply powers of the same base, add their exponents. Add 2 and 7 to get 9.

$$\left(-a^{2}\right)^{3}+a^{3}+a^{9}-5a^{9}$$

Combine a^{9} and -5a^{9} to get -4a^{9}.

$$\left(-a^{2}\right)^{3}+a^{3}-4a^{9}$$

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

$$\left(-1\right)^{3}\left(a^{2}\right)^{3}+a^{3}-4a^{9}$$

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

$$\left(-1\right)^{3}a^{6}+a^{3}-4a^{9}$$

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

$$-a^{6}+a^{3}-4a^{9}$$