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

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

Evaluate

$$a^{5}b^{7}$$

Solution Steps

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

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

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

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

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\left(-a^{2}\right)b^{7}\left(-a\right)^{3}$$

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

$$-a^{2}b^{7}\left(-1\right)^{3}a^{3}$$

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

$$-a^{2}b^{7}\left(-1\right)a^{3}$$

Multiply -1 and -1 to get 1.

$$a^{2}b^{7}a^{3}$$

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

$$a^{5}b^{7}$$

Expand

$$a^{5}b^{7}$$

Solution Steps

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

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

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

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

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\left(-a^{2}\right)b^{7}\left(-a\right)^{3}$$

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

$$-a^{2}b^{7}\left(-1\right)^{3}a^{3}$$

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

$$-a^{2}b^{7}\left(-1\right)a^{3}$$

Multiply -1 and -1 to get 1.

$$a^{2}b^{7}a^{3}$$

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

$$a^{5}b^{7}$$