Solve frac{(-2ab^{2})^3div0.5}{8a(8b^5)}-0.5a^2b-ba^2/4

$$\frac { ( - 2 a b ^ { 2 } ) ^ { 3 } \div 0.5 } { 8 a ( 8 b ^ { 5 } ) } - 0.5 a ^ { 2 } b - \frac { b a ^ { 2 } } { 4 }$$

Evaluate

$$-ba^{2}$$

Short Solution Steps

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

$$\frac{\frac{\left(-2\right)^{3}a^{3}\left(b^{2}\right)^{3}}{0.5}}{8a\times 8b^{5}}-0.5a^{2}b-\frac{ba^{2}}{4}$$

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

$$\frac{\frac{\left(-2\right)^{3}a^{3}b^{6}}{0.5}}{8a\times 8b^{5}}-0.5a^{2}b-\frac{ba^{2}}{4}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{\frac{-8a^{3}b^{6}}{0.5}}{8a\times 8b^{5}}-0.5a^{2}b-\frac{ba^{2}}{4}$$

Divide -8a^{3}b^{6} by 0.5 to get -16a^{3}b^{6}.

$$\frac{-16a^{3}b^{6}}{8a\times 8b^{5}}-0.5a^{2}b-\frac{ba^{2}}{4}$$

Multiply 8 and 8 to get 64.

$$\frac{-16a^{3}b^{6}}{64ab^{5}}-0.5a^{2}b-\frac{ba^{2}}{4}$$

Cancel out 16ab^{5} in both numerator and denominator.

$$\frac{-ba^{2}}{4}-0.5a^{2}b-\frac{ba^{2}}{4}$$

Since \frac{-ba^{2}}{4} and \frac{ba^{2}}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-ba^{2}-ba^{2}}{4}-0.5a^{2}b$$

Combine like terms in -ba^{2}-ba^{2}.

$$\frac{-2ba^{2}}{4}-0.5a^{2}b$$

Divide -2ba^{2} by 4 to get -\frac{1}{2}ba^{2}.

$$-\frac{1}{2}ba^{2}-0.5a^{2}b$$

Combine -\frac{1}{2}ba^{2} and -0.5a^{2}b to get -ba^{2}.

$$-ba^{2}$$

Expand

$$-ba^{2}$$

Short Solution Steps

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

$$\frac{\frac{\left(-2\right)^{3}a^{3}\left(b^{2}\right)^{3}}{0.5}}{8a\times 8b^{5}}-0.5a^{2}b-\frac{ba^{2}}{4}$$

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

$$\frac{\frac{\left(-2\right)^{3}a^{3}b^{6}}{0.5}}{8a\times 8b^{5}}-0.5a^{2}b-\frac{ba^{2}}{4}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{\frac{-8a^{3}b^{6}}{0.5}}{8a\times 8b^{5}}-0.5a^{2}b-\frac{ba^{2}}{4}$$

Divide -8a^{3}b^{6} by 0.5 to get -16a^{3}b^{6}.

$$\frac{-16a^{3}b^{6}}{8a\times 8b^{5}}-0.5a^{2}b-\frac{ba^{2}}{4}$$

Multiply 8 and 8 to get 64.

$$\frac{-16a^{3}b^{6}}{64ab^{5}}-0.5a^{2}b-\frac{ba^{2}}{4}$$

Cancel out 16ab^{5} in both numerator and denominator.

$$\frac{-ba^{2}}{4}-0.5a^{2}b-\frac{ba^{2}}{4}$$

Since \frac{-ba^{2}}{4} and \frac{ba^{2}}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-ba^{2}-ba^{2}}{4}-0.5a^{2}b$$

Combine like terms in -ba^{2}-ba^{2}.

$$\frac{-2ba^{2}}{4}-0.5a^{2}b$$

Divide -2ba^{2} by 4 to get -\frac{1}{2}ba^{2}.

$$-\frac{1}{2}ba^{2}-0.5a^{2}b$$

Combine -\frac{1}{2}ba^{2} and -0.5a^{2}b to get -ba^{2}.

$$-ba^{2}$$