Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\sqrt{7\sqrt{7\sqrt{7\sqrt{7\sqrt{7}}}$$

Answer

$$16807*sq^3*r^5*t^5*s^2*q^2$$

Solution


Take out the constants.
\[(7\times 7\times 7\times 7\times 7)rrrrrtttttssqqsqsqsq\]
Simplify  \(7\times 7\)  to  \(49\).
\[(49\times 49\times 7)rrrrrtttttssqqsqsqsq\]
Simplify  \(49\times 49\)  to  \(2401\).
\[(2401\times 7)rrrrrtttttssqqsqsqsq\]
Simplify  \(2401\times 7\)  to  \(16807\).
\[16807rrrrrtttttssqqsqsqsq\]
Simplify.
\[16807{r}^{5}{t}^{5}{s}^{2}{q}^{2}sqsqsq\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[16807{r}^{5}{t}^{5}{s}^{2}{q}^{2}{sq}^{3}\]
Regroup terms.
\[16807{sq}^{3}{r}^{5}{t}^{5}{s}^{2}{q}^{2}\]
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