Solve -5ab^5*(-10a^3b)^2

$$- 5 a b ^ { 5 } \cdot ( - 10 a ^ { 3 } b ) ^ { 2 }$$

Evaluate

$$-500\left(ab\right)^{7}$$

Solution Steps

Expand \left(-10a^{3}b\right)^{2}.

$$-5ab^{5}\left(-10\right)^{2}\left(a^{3}\right)^{2}b^{2}$$

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

$$-5ab^{5}\left(-10\right)^{2}a^{6}b^{2}$$

Calculate -10 to the power of 2 and get 100.

$$-5ab^{5}\times 100a^{6}b^{2}$$

Multiply -5 and 100 to get -500.

$$-500ab^{5}a^{6}b^{2}$$

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

$$-500a^{7}b^{5}b^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$-500a^{7}b^{7}$$

Expand

$$-500\left(ab\right)^{7}$$

Solution Steps

Expand \left(-10a^{3}b\right)^{2}.

$$-5ab^{5}\left(-10\right)^{2}\left(a^{3}\right)^{2}b^{2}$$

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

$$-5ab^{5}\left(-10\right)^{2}a^{6}b^{2}$$

Calculate -10 to the power of 2 and get 100.

$$-5ab^{5}\times 100a^{6}b^{2}$$

Multiply -5 and 100 to get -500.

$$-500ab^{5}a^{6}b^{2}$$

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

$$-500a^{7}b^{5}b^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$-500a^{7}b^{7}$$