Solve (-4ab^3)(-3/8ab)-(1/2ab^2)^2

$$( - 4 a b ^ { 3 } ) ( - \frac { 3 } { 8 } a b ) - ( \frac { 1 } { 2 } a b ^ { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{5a^{2}b^{4}}{4}$$

Solution Steps

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

$$-4a^{2}b^{3}\left(-\frac{3}{8}\right)b-\left(\frac{1}{2}ab^{2}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$-4a^{2}b^{4}\left(-\frac{3}{8}\right)-\left(\frac{1}{2}ab^{2}\right)^{2}$$

Multiply -4 and -\frac{3}{8} to get \frac{3}{2}.

$$\frac{3}{2}a^{2}b^{4}-\left(\frac{1}{2}ab^{2}\right)^{2}$$

Expand \left(\frac{1}{2}ab^{2}\right)^{2}.

$$\frac{3}{2}a^{2}b^{4}-\left(\frac{1}{2}\right)^{2}a^{2}\left(b^{2}\right)^{2}$$

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

$$\frac{3}{2}a^{2}b^{4}-\left(\frac{1}{2}\right)^{2}a^{2}b^{4}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{3}{2}a^{2}b^{4}-\frac{1}{4}a^{2}b^{4}$$

Combine \frac{3}{2}a^{2}b^{4} and -\frac{1}{4}a^{2}b^{4} to get \frac{5}{4}a^{2}b^{4}.

$$\frac{5}{4}a^{2}b^{4}$$

Expand

$$\frac{5a^{2}b^{4}}{4}$$

Solution Steps

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

$$-4a^{2}b^{3}\left(-\frac{3}{8}\right)b-\left(\frac{1}{2}ab^{2}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$-4a^{2}b^{4}\left(-\frac{3}{8}\right)-\left(\frac{1}{2}ab^{2}\right)^{2}$$

Multiply -4 and -\frac{3}{8} to get \frac{3}{2}.

$$\frac{3}{2}a^{2}b^{4}-\left(\frac{1}{2}ab^{2}\right)^{2}$$

Expand \left(\frac{1}{2}ab^{2}\right)^{2}.

$$\frac{3}{2}a^{2}b^{4}-\left(\frac{1}{2}\right)^{2}a^{2}\left(b^{2}\right)^{2}$$

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

$$\frac{3}{2}a^{2}b^{4}-\left(\frac{1}{2}\right)^{2}a^{2}b^{4}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{3}{2}a^{2}b^{4}-\frac{1}{4}a^{2}b^{4}$$

Combine \frac{3}{2}a^{2}b^{4} and -\frac{1}{4}a^{2}b^{4} to get \frac{5}{4}a^{2}b^{4}.

$$\frac{5}{4}a^{2}b^{4}$$