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

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

Evaluate

$$2a^{11}$$

Solution Steps

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

$$a^{6}a^{5}+\left(\left(-a\right)^{2}\right)^{5}a$$

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$a^{11}+\left(\left(-a\right)^{2}\right)^{5}a$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$a^{11}+\left(-a\right)^{10}a$$

Expand \left(-a\right)^{10}.

$$a^{11}+\left(-1\right)^{10}a^{10}a$$

Calculate -1 to the power of 10 and get 1.

$$a^{11}+1a^{10}a$$

To multiply powers of the same base, add their exponents. Add 10 and 1 to get 11.

$$a^{11}+1a^{11}$$

Combine a^{11} and 1a^{11} to get 2a^{11}.

$$2a^{11}$$

Expand

$$2a^{11}$$

Solution Steps

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

$$a^{6}a^{5}+\left(\left(-a\right)^{2}\right)^{5}a$$

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$a^{11}+\left(\left(-a\right)^{2}\right)^{5}a$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$a^{11}+\left(-a\right)^{10}a$$

Expand \left(-a\right)^{10}.

$$a^{11}+\left(-1\right)^{10}a^{10}a$$

Calculate -1 to the power of 10 and get 1.

$$a^{11}+1a^{10}a$$

To multiply powers of the same base, add their exponents. Add 10 and 1 to get 11.

$$a^{11}+1a^{11}$$

Combine a^{11} and 1a^{11} to get 2a^{11}.

$$2a^{11}$$