Solve 4a^3b^2(-5ab)^2

$$4 a ^ { 3 } b ^ { 2 } ( - 5 a b ) ^ { 2 }$$

Evaluate

$$100b^{4}a^{5}$$

Solution Steps

Expand \left(-5ab\right)^{2}.

$$4a^{3}b^{2}\left(-5\right)^{2}a^{2}b^{2}$$

Calculate -5 to the power of 2 and get 25.

$$4a^{3}b^{2}\times 25a^{2}b^{2}$$

Multiply 4 and 25 to get 100.

$$100a^{3}b^{2}a^{2}b^{2}$$

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

$$100a^{5}b^{2}b^{2}$$

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

$$100a^{5}b^{4}$$

Expand

$$100b^{4}a^{5}$$

Solution Steps

Expand \left(-5ab\right)^{2}.

$$4a^{3}b^{2}\left(-5\right)^{2}a^{2}b^{2}$$

Calculate -5 to the power of 2 and get 25.

$$4a^{3}b^{2}\times 25a^{2}b^{2}$$

Multiply 4 and 25 to get 100.

$$100a^{3}b^{2}a^{2}b^{2}$$

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

$$100a^{5}b^{2}b^{2}$$

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

$$100a^{5}b^{4}$$