Solve -(4a^3b)^2*3a^5/8b^4

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

Evaluate

$$-\frac{6a^{11}}{b^{2}}$$

Short Solution Steps

Expand \left(4a^{3}b\right)^{2}.

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

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

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

Calculate 4 to the power of 2 and get 16.

$$\frac{\left(-16a^{6}b^{2}\right)\times 3a^{5}}{8b^{4}}$$

Factor the expressions that are not already factored.

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

Cancel out 8b^{2} in both numerator and denominator.

$$\frac{-2\times 3a^{5}a^{6}}{b^{2}}$$

Expand the expression.

$$\frac{-6a^{11}}{b^{2}}$$

Expand

$$-\frac{6a^{11}}{b^{2}}$$

Short Solution Steps

Expand \left(4a^{3}b\right)^{2}.

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

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

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

Calculate 4 to the power of 2 and get 16.

$$\frac{\left(-16a^{6}b^{2}\right)\times 3a^{5}}{8b^{4}}$$

Factor the expressions that are not already factored.

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

Cancel out 8b^{2} in both numerator and denominator.

$$\frac{-2\times 3a^{5}a^{6}}{b^{2}}$$

Expand the expression.

$$\frac{-6a^{11}}{b^{2}}$$