Solve 8(a^2)^2*(-b)^2*(-a^2b)

$$8 ( a ^ { 2 } ) ^ { 2 } \cdot ( - b ) ^ { 2 } \cdot ( - a ^ { 2 } b )$$

Evaluate

$$-8b^{3}a^{6}$$

Solution Steps

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

$$8a^{4}\left(-b\right)^{2}\left(-a^{2}\right)b$$

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

$$8a^{4}b^{2}\left(-a^{2}\right)b$$

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

$$8a^{4}b^{3}\left(-a^{2}\right)$$

Multiply 8 and -1 to get -8.

$$-8a^{4}b^{3}a^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$-8a^{6}b^{3}$$

Expand

$$-8b^{3}a^{6}$$

Solution Steps

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

$$8a^{4}\left(-b\right)^{2}\left(-a^{2}\right)b$$

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

$$8a^{4}b^{2}\left(-a^{2}\right)b$$

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

$$8a^{4}b^{3}\left(-a^{2}\right)$$

Multiply 8 and -1 to get -8.

$$-8a^{4}b^{3}a^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$-8a^{6}b^{3}$$