Solve S=(w^2*r)*(w^2*r_{1})

$$S = ( w ^ { 2 } \cdot r ) \cdot ( w ^ { 2 } \cdot r _ { 1 } )$$

Solve for r

$$\left\{\begin{matrix}r=\frac{S}{r_{1}w^{4}}\text{, }&r_{1}\neq 0\text{ and }w\neq 0\\r\in \mathrm{R}\text{, }&\left(r_{1}=0\text{ or }w=0\right)\text{ and }S=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$S=w^{4}rr_{1}$$

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

$$w^{4}rr_{1}=S$$

The equation is in standard form.

$$r_{1}w^{4}r=S$$

Divide both sides by w^{4}r_{1}.

$$\frac{r_{1}w^{4}r}{r_{1}w^{4}}=\frac{S}{r_{1}w^{4}}$$

Dividing by w^{4}r_{1} undoes the multiplication by w^{4}r_{1}.

$$r=\frac{S}{r_{1}w^{4}}$$

Solve for S

$$S=rr_{1}w^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$S=w^{4}rr_{1}$$