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

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

Evaluate

$$-\left(ab\right)^{7}$$

Solution Steps

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

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

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

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

Calculate -a^{3} to the power of 2 and get \left(a^{3}\right)^{2}.

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

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

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

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

$$a^{6}b^{7}\left(-a\right)$$

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

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

Expand

$$-\left(ab\right)^{7}$$

Solution Steps

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

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

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

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

Calculate -a^{3} to the power of 2 and get \left(a^{3}\right)^{2}.

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

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

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

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

$$a^{6}b^{7}\left(-a\right)$$

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

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