Solve u/lambda=6.6*10^-34*3*10^8/4950*10^-10=

$$\frac { u } { \lambda } = \frac { 6.6 \times 10 ^ { - 34 } \times 3 \times 10 ^ { 8 } } { 4950 \times 10 ^ { - 10 } } =$$

Solve for u

$$u=\frac{\lambda }{2500000000000000000}$$

$$\lambda \neq 0$$

Solution Steps

Multiply both sides of the equation by \lambda .

$$u=\frac{200000000}{99}\lambda \times 6.6\times 10^{-34}\times 3\times 10^{8}$$

To multiply powers of the same base, add their exponents. Add -34 and 8 to get -26.

$$u=\frac{200000000}{99}\lambda \times 6.6\times 10^{-26}\times 3$$

Multiply \frac{200000000}{99} and 6.6 to get \frac{40000000}{3}.

$$u=\frac{40000000}{3}\lambda \times 10^{-26}\times 3$$

Calculate 10 to the power of -26 and get \frac{1}{100000000000000000000000000}.

$$u=\frac{40000000}{3}\lambda \times \frac{1}{100000000000000000000000000}\times 3$$

Multiply \frac{40000000}{3} and \frac{1}{100000000000000000000000000} to get \frac{1}{7500000000000000000}.

$$u=\frac{1}{7500000000000000000}\lambda \times 3$$

Multiply \frac{1}{7500000000000000000} and 3 to get \frac{1}{2500000000000000000}.

$$u=\frac{1}{2500000000000000000}\lambda$$

Solve for λ

$$\lambda =2500000000000000000u$$

$$u\neq 0$$

Steps for Solving Linear Equation

Variable \lambda cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by \lambda .

$$u=\frac{200000000}{99}\lambda \times 6.6\times 10^{-34}\times 3\times 10^{8}$$

To multiply powers of the same base, add their exponents. Add -34 and 8 to get -26.

$$u=\frac{200000000}{99}\lambda \times 6.6\times 10^{-26}\times 3$$

Multiply \frac{200000000}{99} and 6.6 to get \frac{40000000}{3}.

$$u=\frac{40000000}{3}\lambda \times 10^{-26}\times 3$$

Calculate 10 to the power of -26 and get \frac{1}{100000000000000000000000000}.

$$u=\frac{40000000}{3}\lambda \times \frac{1}{100000000000000000000000000}\times 3$$

Multiply \frac{40000000}{3} and \frac{1}{100000000000000000000000000} to get \frac{1}{7500000000000000000}.

$$u=\frac{1}{7500000000000000000}\lambda \times 3$$

Multiply \frac{1}{7500000000000000000} and 3 to get \frac{1}{2500000000000000000}.

$$u=\frac{1}{2500000000000000000}\lambda$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{2500000000000000000}\lambda =u$$

Multiply both sides by 2500000000000000000.

$$\frac{\frac{1}{2500000000000000000}\lambda }{\frac{1}{2500000000000000000}}=\frac{u}{\frac{1}{2500000000000000000}}$$

Dividing by \frac{1}{2500000000000000000} undoes the multiplication by \frac{1}{2500000000000000000}.

$$\lambda =\frac{u}{\frac{1}{2500000000000000000}}$$

Divide u by \frac{1}{2500000000000000000} by multiplying u by the reciprocal of \frac{1}{2500000000000000000}.

$$\lambda =2500000000000000000u$$

Variable \lambda cannot be equal to 0.

$$\lambda =2500000000000000000u\text{, }\lambda \neq 0$$