Solve (a/2)^3(4b)^3/(-2a^3)(b^2)

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

Evaluate

$$-4b$$

Solution Steps

To raise \frac{a}{2} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(4b\right)^{3}.

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

Calculate 4 to the power of 3 and get 64.

$$\frac{\frac{a^{3}}{2^{3}}\times 64b^{3}}{-2a^{3}b^{2}}$$

Express \frac{a^{3}}{2^{3}}\times 64 as a single fraction.

$$\frac{\frac{a^{3}\times 64}{2^{3}}b^{3}}{-2a^{3}b^{2}}$$

Express \frac{a^{3}\times 64}{2^{3}}b^{3} as a single fraction.

$$\frac{\frac{a^{3}\times 64b^{3}}{2^{3}}}{-2a^{3}b^{2}}$$

Express \frac{\frac{a^{3}\times 64b^{3}}{2^{3}}}{-2a^{3}b^{2}} as a single fraction.

$$\frac{a^{3}\times 64b^{3}}{2^{3}\left(-2\right)a^{3}b^{2}}$$

Cancel out 2b^{2}a^{3} in both numerator and denominator.

$$\frac{32b}{-2^{3}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{-32b}{2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{-32b}{8}$$

Divide -32b by 8 to get -4b.

$$-4b$$

Expand

$$-4b$$

Solution Steps

To raise \frac{a}{2} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(4b\right)^{3}.

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

Calculate 4 to the power of 3 and get 64.

$$\frac{\frac{a^{3}}{2^{3}}\times 64b^{3}}{-2a^{3}b^{2}}$$

Express \frac{a^{3}}{2^{3}}\times 64 as a single fraction.

$$\frac{\frac{a^{3}\times 64}{2^{3}}b^{3}}{-2a^{3}b^{2}}$$

Express \frac{a^{3}\times 64}{2^{3}}b^{3} as a single fraction.

$$\frac{\frac{a^{3}\times 64b^{3}}{2^{3}}}{-2a^{3}b^{2}}$$

Express \frac{\frac{a^{3}\times 64b^{3}}{2^{3}}}{-2a^{3}b^{2}} as a single fraction.

$$\frac{a^{3}\times 64b^{3}}{2^{3}\left(-2\right)a^{3}b^{2}}$$

Cancel out 2b^{2}a^{3} in both numerator and denominator.

$$\frac{32b}{-2^{3}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{-32b}{2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{-32b}{8}$$

Divide -32b by 8 to get -4b.

$$-4b$$