Solve P(L)3!*P(E)2!*P(A)3!=72.H

$$P ( L ) 3 ! \times P ( E ) 2 ! \times P ( A ) 3 ! = 72 . H$$

Solve for A

$$A=\frac{1}{ELP^{3}}$$

$$E\neq 0\text{ and }L\neq 0\text{ and }P\neq 0$$

Steps for Solving Linear Equation

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

$$P^{2}L\times 3!E\times 2!PA\times 3!=72$$

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

$$P^{3}L\times 3!E\times 2!A\times 3!=72$$

Multiply 3! and 3! to get \left(3!\right)^{2}.

$$P^{3}L\times \left(3!\right)^{2}E\times 2!A=72$$

The factorial of 3 is 6.

$$P^{3}L\times 6^{2}E\times 2!A=72$$

Calculate 6 to the power of 2 and get 36.

$$P^{3}L\times 36E\times 2!A=72$$

The factorial of 2 is 2.

$$P^{3}L\times 36E\times 2A=72$$

Multiply 36 and 2 to get 72.

$$P^{3}L\times 72EA=72$$

The equation is in standard form.

$$72ELP^{3}A=72$$

Divide both sides by 72P^{3}LE.

$$\frac{72ELP^{3}A}{72ELP^{3}}=\frac{72}{72ELP^{3}}$$

Dividing by 72P^{3}LE undoes the multiplication by 72P^{3}LE.

$$A=\frac{72}{72ELP^{3}}$$

Divide 72 by 72P^{3}LE.

$$A=\frac{1}{ELP^{3}}$$

Solve for E

$$E=\frac{1}{ALP^{3}}$$

$$L\neq 0\text{ and }P\neq 0\text{ and }A\neq 0$$

Steps for Solving Linear Equation

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

$$P^{2}L\times 3!E\times 2!PA\times 3!=72$$

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

$$P^{3}L\times 3!E\times 2!A\times 3!=72$$

Multiply 3! and 3! to get \left(3!\right)^{2}.

$$P^{3}L\times \left(3!\right)^{2}E\times 2!A=72$$

The factorial of 3 is 6.

$$P^{3}L\times 6^{2}E\times 2!A=72$$

Calculate 6 to the power of 2 and get 36.

$$P^{3}L\times 36E\times 2!A=72$$

The factorial of 2 is 2.

$$P^{3}L\times 36E\times 2A=72$$

Multiply 36 and 2 to get 72.

$$P^{3}L\times 72EA=72$$

The equation is in standard form.

$$72ALP^{3}E=72$$

Divide both sides by 72P^{3}LA.

$$\frac{72ALP^{3}E}{72ALP^{3}}=\frac{72}{72ALP^{3}}$$

Dividing by 72P^{3}LA undoes the multiplication by 72P^{3}LA.

$$E=\frac{72}{72ALP^{3}}$$

Divide 72 by 72P^{3}LA.

$$E=\frac{1}{ALP^{3}}$$