Solve {left(frac{a/2right)}^3left(4bright)^3}{-2a^3b^3}

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

Evaluate

$$-4$$

Solution Steps

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

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

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

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

Calculate 4 to the power of 3 and get 64.

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

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

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

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

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

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

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

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

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

Calculate 2 to the power of 3 and get 8.

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

Divide 32 by -8 to get -4.

$$-4$$

Factor

$$-4$$