Solve 10^5/P_{V}*16^frac{5{3}}=4.2^frac{3{3}}

$$\frac { 10 ^ { 5 } } { P _ { V } } \cdot 16 ^ { \frac { 5 } { 3 } } = 4.2 ^ { \frac { 3 } { 3 } }$$

Solve for P_V

$$P_{V} = \frac{32000000 \cdot 2 ^ {\frac{2}{3}}}{21} \approx 2418896.841094399$$

Steps for Solving Linear Equation

Variable P_{V} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by P_{V}.

$$10^{5}\times 16^{\frac{5}{3}}=P_{V}\times 4.2^{\frac{3}{3}}$$

Calculate 10 to the power of 5 and get 100000.

$$100000\times 16^{\frac{5}{3}}=P_{V}\times 4.2^{\frac{3}{3}}$$

Divide 3 by 3 to get 1.

$$100000\times 16^{\frac{5}{3}}=P_{V}\times 4.2^{1}$$

Calculate 4.2 to the power of 1 and get 4.2.

$$100000\times 16^{\frac{5}{3}}=P_{V}\times 4.2$$

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

$$P_{V}\times 4.2=100000\times 16^{\frac{5}{3}}$$

The equation is in standard form.

$$4.2P_{V}=6400000\times 2^{\frac{2}{3}}$$

Divide both sides of the equation by 4.2, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{4.2P_{V}}{4.2}=\frac{6400000\times 2^{\frac{2}{3}}}{4.2}$$

Dividing by 4.2 undoes the multiplication by 4.2.

$$P_{V}=\frac{6400000\times 2^{\frac{2}{3}}}{4.2}$$

Divide 6400000\times 2^{\frac{2}{3}} by 4.2 by multiplying 6400000\times 2^{\frac{2}{3}} by the reciprocal of 4.2.

$$P_{V}=\frac{32000000\times 2^{\frac{2}{3}}}{21}$$