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

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

Evaluate

$$8a^{8}b^{9}$$

Solution Steps

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

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

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

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

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

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

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

$$\left(-a^{2}\right)\left(-2\right)^{3}a^{6}b^{9}$$

Calculate -2 to the power of 3 and get -8.

$$\left(-a^{2}\right)\left(-8\right)a^{6}b^{9}$$

Multiply -1 and -8 to get 8.

$$8a^{2}a^{6}b^{9}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$8a^{8}b^{9}$$

Expand

$$8a^{8}b^{9}$$

Solution Steps

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

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

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

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

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

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

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

$$\left(-a^{2}\right)\left(-2\right)^{3}a^{6}b^{9}$$

Calculate -2 to the power of 3 and get -8.

$$\left(-a^{2}\right)\left(-8\right)a^{6}b^{9}$$

Multiply -1 and -8 to get 8.

$$8a^{2}a^{6}b^{9}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$8a^{8}b^{9}$$