Solve a+2a+3a-a*a^2*a^3+(-a^2)^3

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

Evaluate

$$6a-2a^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

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

Combine a and 2a to get 3a.

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

Combine 3a and 3a to get 6a.

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

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

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

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

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

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

$$6a-a^{6}-a^{6}$$

Combine -a^{6} and -a^{6} to get -2a^{6}.

$$6a-2a^{6}$$

Expand

$$6a-2a^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

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

Combine a and 2a to get 3a.

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

Combine 3a and 3a to get 6a.

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

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

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

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

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

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

$$6a-a^{6}-a^{6}$$

Combine -a^{6} and -a^{6} to get -2a^{6}.

$$6a-2a^{6}$$