Solve v=(0.040mm)^3

$$v = ( 0.040 mm ) ^ { 3 }$$

Solve for v

$$v=\frac{m^{6}}{15625}$$

Solution Steps

Multiply m and m to get m^{2}.

$$v=\left(0.04m^{2}\right)^{3}$$

Expand \left(0.04m^{2}\right)^{3}.

$$v=0.04^{3}\left(m^{2}\right)^{3}$$

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

$$v=0.04^{3}m^{6}$$

Calculate 0.04 to the power of 3 and get 0.000064.

$$v=0.000064m^{6}$$

Solve for m

$$m=5\sqrt[6]{v}$$

$$m=-5\sqrt[6]{v}\text{, }v\geq 0$$