Solve (4/3-2/5m^10)^3=

$$( \frac { 4 } { 3 } - \frac { 2 } { 5 } m ^ { 10 } ) ^ { 3 } =$$

Evaluate

$$\frac{8\left(10-3m^{10}\right)^{3}}{3375}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(\frac{4}{3}-\frac{2}{5}m^{10}\right)^{3}.

$$\frac{64}{27}-\frac{32}{15}m^{10}+\frac{16}{25}\left(m^{10}\right)^{2}-\frac{8}{125}\left(m^{10}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 10 and 2 to get 20.

$$\frac{64}{27}-\frac{32}{15}m^{10}+\frac{16}{25}m^{20}-\frac{8}{125}\left(m^{10}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 10 and 3 to get 30.

$$\frac{64}{27}-\frac{32}{15}m^{10}+\frac{16}{25}m^{20}-\frac{8}{125}m^{30}$$

Expand

$$-\frac{8m^{30}}{125}+\frac{16m^{20}}{25}-\frac{32m^{10}}{15}+\frac{64}{27}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(\frac{4}{3}-\frac{2}{5}m^{10}\right)^{3}.

$$\frac{64}{27}-\frac{32}{15}m^{10}+\frac{16}{25}\left(m^{10}\right)^{2}-\frac{8}{125}\left(m^{10}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 10 and 2 to get 20.

$$\frac{64}{27}-\frac{32}{15}m^{10}+\frac{16}{25}m^{20}-\frac{8}{125}\left(m^{10}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 10 and 3 to get 30.

$$\frac{64}{27}-\frac{32}{15}m^{10}+\frac{16}{25}m^{20}-\frac{8}{125}m^{30}$$