Solve (-8a^{3}x)(+3/4ab)-[(-2/3a^2c)^2:(+4/5ac)+(-1/6a^3c)+(-6a^4bx)]

$$( - 8 a ^ { 3 } x ) ( + \frac { 3 } { 4 } a b ) - [ ( - \frac { 2 } { 3 } a ^ { 2 } c ) ^ { 2 } : ( + \frac { 4 } { 5 } a c ) + ( - \frac { 1 } { 6 } a ^ { 3 } c ) + ( - 6 a ^ { 4 } b x ) ]$$

Evaluate

$$-\frac{7ca^{3}}{18}$$

Solution Steps

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

$$-8a^{4}x\times \frac{3}{4}b-\left(\frac{\left(-\frac{2}{3}a^{2}c\right)^{2}}{\frac{4}{5}ac}-\frac{1}{6}a^{3}c-6a^{4}bx\right)$$

Multiply -8 and \frac{3}{4} to get -6.

$$-6a^{4}xb-\left(\frac{\left(-\frac{2}{3}a^{2}c\right)^{2}}{\frac{4}{5}ac}-\frac{1}{6}a^{3}c-6a^{4}bx\right)$$

Expand \left(-\frac{2}{3}a^{2}c\right)^{2}.

$$-6a^{4}xb-\left(\frac{\left(-\frac{2}{3}\right)^{2}\left(a^{2}\right)^{2}c^{2}}{\frac{4}{5}ac}-\frac{1}{6}a^{3}c-6a^{4}bx\right)$$

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

$$-6a^{4}xb-\left(\frac{\left(-\frac{2}{3}\right)^{2}a^{4}c^{2}}{\frac{4}{5}ac}-\frac{1}{6}a^{3}c-6a^{4}bx\right)$$

Calculate -\frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$-6a^{4}xb-\left(\frac{\frac{4}{9}a^{4}c^{2}}{\frac{4}{5}ac}-\frac{1}{6}a^{3}c-6a^{4}bx\right)$$

Cancel out ac in both numerator and denominator.

$$-6a^{4}xb-\left(\frac{\frac{4}{9}ca^{3}}{\frac{4}{5}}-\frac{1}{6}a^{3}c-6a^{4}bx\right)$$

Divide \frac{4}{9}ca^{3} by \frac{4}{5} by multiplying \frac{4}{9}ca^{3} by the reciprocal of \frac{4}{5}.

$$-6a^{4}xb-\left(\frac{\frac{4}{9}ca^{3}\times 5}{4}-\frac{1}{6}a^{3}c-6a^{4}bx\right)$$

Multiply \frac{4}{9} and 5 to get \frac{20}{9}.

$$-6a^{4}xb-\left(\frac{\frac{20}{9}ca^{3}}{4}-\frac{1}{6}a^{3}c-6a^{4}bx\right)$$

Divide \frac{20}{9}ca^{3} by 4 to get \frac{5}{9}ca^{3}.

$$-6a^{4}xb-\left(\frac{5}{9}ca^{3}-\frac{1}{6}a^{3}c-6a^{4}bx\right)$$

Combine \frac{5}{9}ca^{3} and -\frac{1}{6}a^{3}c to get \frac{7}{18}ca^{3}.

$$-6a^{4}xb-\left(\frac{7}{18}ca^{3}-6a^{4}bx\right)$$

To find the opposite of \frac{7}{18}ca^{3}-6a^{4}bx, find the opposite of each term.

$$-6a^{4}xb-\frac{7}{18}ca^{3}+6a^{4}bx$$

Combine -6a^{4}xb and 6a^{4}bx to get 0.

$$-\frac{7}{18}ca^{3}$$

Expand

$$-\frac{7ca^{3}}{18}$$

Solution Steps

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

$$-8a^{4}x\times \frac{3}{4}b-\left(\frac{\left(-\frac{2}{3}a^{2}c\right)^{2}}{\frac{4}{5}ac}-\frac{1}{6}a^{3}c-6a^{4}bx\right)$$

Multiply -8 and \frac{3}{4} to get -6.

$$-6a^{4}xb-\left(\frac{\left(-\frac{2}{3}a^{2}c\right)^{2}}{\frac{4}{5}ac}-\frac{1}{6}a^{3}c-6a^{4}bx\right)$$

Expand \left(-\frac{2}{3}a^{2}c\right)^{2}.

$$-6a^{4}xb-\left(\frac{\left(-\frac{2}{3}\right)^{2}\left(a^{2}\right)^{2}c^{2}}{\frac{4}{5}ac}-\frac{1}{6}a^{3}c-6a^{4}bx\right)$$

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

$$-6a^{4}xb-\left(\frac{\left(-\frac{2}{3}\right)^{2}a^{4}c^{2}}{\frac{4}{5}ac}-\frac{1}{6}a^{3}c-6a^{4}bx\right)$$

Calculate -\frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$-6a^{4}xb-\left(\frac{\frac{4}{9}a^{4}c^{2}}{\frac{4}{5}ac}-\frac{1}{6}a^{3}c-6a^{4}bx\right)$$

Cancel out ac in both numerator and denominator.

$$-6a^{4}xb-\left(\frac{\frac{4}{9}ca^{3}}{\frac{4}{5}}-\frac{1}{6}a^{3}c-6a^{4}bx\right)$$

Divide \frac{4}{9}ca^{3} by \frac{4}{5} by multiplying \frac{4}{9}ca^{3} by the reciprocal of \frac{4}{5}.

$$-6a^{4}xb-\left(\frac{\frac{4}{9}ca^{3}\times 5}{4}-\frac{1}{6}a^{3}c-6a^{4}bx\right)$$

Multiply \frac{4}{9} and 5 to get \frac{20}{9}.

$$-6a^{4}xb-\left(\frac{\frac{20}{9}ca^{3}}{4}-\frac{1}{6}a^{3}c-6a^{4}bx\right)$$

Divide \frac{20}{9}ca^{3} by 4 to get \frac{5}{9}ca^{3}.

$$-6a^{4}xb-\left(\frac{5}{9}ca^{3}-\frac{1}{6}a^{3}c-6a^{4}bx\right)$$

Combine \frac{5}{9}ca^{3} and -\frac{1}{6}a^{3}c to get \frac{7}{18}ca^{3}.

$$-6a^{4}xb-\left(\frac{7}{18}ca^{3}-6a^{4}bx\right)$$

To find the opposite of \frac{7}{18}ca^{3}-6a^{4}bx, find the opposite of each term.

$$-6a^{4}xb-\frac{7}{18}ca^{3}+6a^{4}bx$$

Combine -6a^{4}xb and 6a^{4}bx to get 0.

$$-\frac{7}{18}ca^{3}$$