Solve 2a^{3}*(a^{2})-(-a^4)^2*a+a^2*a^7

$$2 a ^ { 3 } \cdot ( a ^ { 2 } ) - ( - a ^ { 4 } ) ^ { 2 } \cdot a + a ^ { 2 } \cdot a ^ { 7 }$$

Evaluate

$$2a^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$2a^{5}-\left(-a^{4}\right)^{2}a+a^{2}a^{7}$$

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

$$2a^{5}-\left(-a^{4}\right)^{2}a+a^{9}$$

Calculate -a^{4} to the power of 2 and get \left(a^{4}\right)^{2}.

$$2a^{5}-\left(a^{4}\right)^{2}a+a^{9}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$2a^{5}-a^{8}a+a^{9}$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$2a^{5}-a^{9}+a^{9}$$

Combine -a^{9} and a^{9} to get 0.

$$2a^{5}$$

Expand

$$2a^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$2a^{5}-\left(-a^{4}\right)^{2}a+a^{2}a^{7}$$

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

$$2a^{5}-\left(-a^{4}\right)^{2}a+a^{9}$$

Calculate -a^{4} to the power of 2 and get \left(a^{4}\right)^{2}.

$$2a^{5}-\left(a^{4}\right)^{2}a+a^{9}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$2a^{5}-a^{8}a+a^{9}$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$2a^{5}-a^{9}+a^{9}$$

Combine -a^{9} and a^{9} to get 0.

$$2a^{5}$$