Solve 5a^2b*(-1/2ab)*(2ab^2)^2

$$5 a ^ { 2 } b \cdot ( - \frac { 1 } { 2 } a b ) \cdot ( 2 a b ^ { 2 } ) ^ { 2 }$$

Evaluate

$$-10a^{5}b^{6}$$

Solution Steps

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

$$5a^{3}b\left(-\frac{1}{2}\right)b\times \left(2ab^{2}\right)^{2}$$

Multiply b and b to get b^{2}.

$$5a^{3}b^{2}\left(-\frac{1}{2}\right)\times \left(2ab^{2}\right)^{2}$$

Multiply 5 and -\frac{1}{2} to get -\frac{5}{2}.

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

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

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

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

$$-\frac{5}{2}a^{3}b^{2}\times 2^{2}a^{2}b^{4}$$

Calculate 2 to the power of 2 and get 4.

$$-\frac{5}{2}a^{3}b^{2}\times 4a^{2}b^{4}$$

Multiply -\frac{5}{2} and 4 to get -10.

$$-10a^{3}b^{2}a^{2}b^{4}$$

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

$$-10a^{5}b^{2}b^{4}$$

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

$$-10a^{5}b^{6}$$

Expand

$$-10a^{5}b^{6}$$

Solution Steps

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

$$5a^{3}b\left(-\frac{1}{2}\right)b\times \left(2ab^{2}\right)^{2}$$

Multiply b and b to get b^{2}.

$$5a^{3}b^{2}\left(-\frac{1}{2}\right)\times \left(2ab^{2}\right)^{2}$$

Multiply 5 and -\frac{1}{2} to get -\frac{5}{2}.

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

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

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

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

$$-\frac{5}{2}a^{3}b^{2}\times 2^{2}a^{2}b^{4}$$

Calculate 2 to the power of 2 and get 4.

$$-\frac{5}{2}a^{3}b^{2}\times 4a^{2}b^{4}$$

Multiply -\frac{5}{2} and 4 to get -10.

$$-10a^{3}b^{2}a^{2}b^{4}$$

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

$$-10a^{5}b^{2}b^{4}$$

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

$$-10a^{5}b^{6}$$