Solve left(a^2b^3right)^2/-frac{1{2}ab^2}2ab

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

Evaluate

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

Solution Steps

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

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

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

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

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

$$\frac{a^{4}b^{6}}{-\frac{1}{2}ab^{2}}\times 2ab$$

Cancel out ab^{2} in both numerator and denominator.

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

Divide a^{3}b^{4} by -\frac{1}{2} by multiplying a^{3}b^{4} by the reciprocal of -\frac{1}{2}.

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

Anything divided by -1 gives its opposite.

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

Multiply -1 and 2 to get -2.

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

Multiply -2 and 2 to get -4.

$$-4a^{3}b^{4}ab$$

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

$$-4a^{4}b^{4}b$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

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

Expand

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

Solution Steps

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

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

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

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

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

$$\frac{a^{4}b^{6}}{-\frac{1}{2}ab^{2}}\times 2ab$$

Cancel out ab^{2} in both numerator and denominator.

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

Divide a^{3}b^{4} by -\frac{1}{2} by multiplying a^{3}b^{4} by the reciprocal of -\frac{1}{2}.

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

Anything divided by -1 gives its opposite.

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

Multiply -1 and 2 to get -2.

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

Multiply -2 and 2 to get -4.

$$-4a^{3}b^{4}ab$$

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

$$-4a^{4}b^{4}b$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

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