Solve -3/4ax^{3}(-a^{2})+(-1/2ax)^{3}+5/8a^2x(-4/5ax^2)+a^3x^3

$$- \frac { 3 } { 4 } a x ^ { 3 } ( - a ^ { 2 } ) + ( - \frac { 1 } { 2 } a x ) ^ { 3 } + \frac { 5 } { 8 } a ^ { 2 } x ( - \frac { 4 } { 5 } a x ^ { 2 } ) + a ^ { 3 } x ^ { 3 }$$

Evaluate

$$\frac{9\left(ax\right)^{3}}{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-\frac{3}{4}ax^{3}\left(-a^{2}\right)+\left(-\frac{1}{2}ax\right)^{3}+\frac{5}{8}a^{3}x\left(-\frac{4}{5}\right)x^{2}+a^{3}x^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-\frac{3}{4}ax^{3}\left(-a^{2}\right)+\left(-\frac{1}{2}ax\right)^{3}+\frac{5}{8}a^{3}x^{3}\left(-\frac{4}{5}\right)+a^{3}x^{3}$$

Multiply -\frac{3}{4} and -1 to get \frac{3}{4}.

$$\frac{3}{4}ax^{3}a^{2}+\left(-\frac{1}{2}ax\right)^{3}+\frac{5}{8}a^{3}x^{3}\left(-\frac{4}{5}\right)+a^{3}x^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{3}{4}a^{3}x^{3}+\left(-\frac{1}{2}ax\right)^{3}+\frac{5}{8}a^{3}x^{3}\left(-\frac{4}{5}\right)+a^{3}x^{3}$$

Expand \left(-\frac{1}{2}ax\right)^{3}.

$$\frac{3}{4}a^{3}x^{3}+\left(-\frac{1}{2}\right)^{3}a^{3}x^{3}+\frac{5}{8}a^{3}x^{3}\left(-\frac{4}{5}\right)+a^{3}x^{3}$$

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

$$\frac{3}{4}a^{3}x^{3}-\frac{1}{8}a^{3}x^{3}+\frac{5}{8}a^{3}x^{3}\left(-\frac{4}{5}\right)+a^{3}x^{3}$$

Combine \frac{3}{4}a^{3}x^{3} and -\frac{1}{8}a^{3}x^{3} to get \frac{5}{8}a^{3}x^{3}.

$$\frac{5}{8}a^{3}x^{3}+\frac{5}{8}a^{3}x^{3}\left(-\frac{4}{5}\right)+a^{3}x^{3}$$

Multiply \frac{5}{8} and -\frac{4}{5} to get -\frac{1}{2}.

$$\frac{5}{8}a^{3}x^{3}-\frac{1}{2}a^{3}x^{3}+a^{3}x^{3}$$

Combine \frac{5}{8}a^{3}x^{3} and -\frac{1}{2}a^{3}x^{3} to get \frac{1}{8}a^{3}x^{3}.

$$\frac{1}{8}a^{3}x^{3}+a^{3}x^{3}$$

Combine \frac{1}{8}a^{3}x^{3} and a^{3}x^{3} to get \frac{9}{8}a^{3}x^{3}.

$$\frac{9}{8}a^{3}x^{3}$$

Expand

$$\frac{9\left(ax\right)^{3}}{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-\frac{3}{4}ax^{3}\left(-a^{2}\right)+\left(-\frac{1}{2}ax\right)^{3}+\frac{5}{8}a^{3}x\left(-\frac{4}{5}\right)x^{2}+a^{3}x^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-\frac{3}{4}ax^{3}\left(-a^{2}\right)+\left(-\frac{1}{2}ax\right)^{3}+\frac{5}{8}a^{3}x^{3}\left(-\frac{4}{5}\right)+a^{3}x^{3}$$

Multiply -\frac{3}{4} and -1 to get \frac{3}{4}.

$$\frac{3}{4}ax^{3}a^{2}+\left(-\frac{1}{2}ax\right)^{3}+\frac{5}{8}a^{3}x^{3}\left(-\frac{4}{5}\right)+a^{3}x^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{3}{4}a^{3}x^{3}+\left(-\frac{1}{2}ax\right)^{3}+\frac{5}{8}a^{3}x^{3}\left(-\frac{4}{5}\right)+a^{3}x^{3}$$

Expand \left(-\frac{1}{2}ax\right)^{3}.

$$\frac{3}{4}a^{3}x^{3}+\left(-\frac{1}{2}\right)^{3}a^{3}x^{3}+\frac{5}{8}a^{3}x^{3}\left(-\frac{4}{5}\right)+a^{3}x^{3}$$

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

$$\frac{3}{4}a^{3}x^{3}-\frac{1}{8}a^{3}x^{3}+\frac{5}{8}a^{3}x^{3}\left(-\frac{4}{5}\right)+a^{3}x^{3}$$

Combine \frac{3}{4}a^{3}x^{3} and -\frac{1}{8}a^{3}x^{3} to get \frac{5}{8}a^{3}x^{3}.

$$\frac{5}{8}a^{3}x^{3}+\frac{5}{8}a^{3}x^{3}\left(-\frac{4}{5}\right)+a^{3}x^{3}$$

Multiply \frac{5}{8} and -\frac{4}{5} to get -\frac{1}{2}.

$$\frac{5}{8}a^{3}x^{3}-\frac{1}{2}a^{3}x^{3}+a^{3}x^{3}$$

Combine \frac{5}{8}a^{3}x^{3} and -\frac{1}{2}a^{3}x^{3} to get \frac{1}{8}a^{3}x^{3}.

$$\frac{1}{8}a^{3}x^{3}+a^{3}x^{3}$$

Combine \frac{1}{8}a^{3}x^{3} and a^{3}x^{3} to get \frac{9}{8}a^{3}x^{3}.

$$\frac{9}{8}a^{3}x^{3}$$