Simplify-2-2-2-2-70-t-1-10-

Question Number 221991 by hardmath last updated on 14/Jun/25

$$\mathrm{Simplify}:\:\:\:\mathrm{2}^{\mathrm{2}} \:\centerdot\:\mathrm{2}^{\mathrm{2}^{\frac{\mathrm{70}\:−\:\boldsymbol{\mathrm{t}}_{\mathrm{1}} }{\mathrm{10}}} \:\:\:=\:\:\:?} \\ $$

Commented by hardmath last updated on 14/Jun/25

$$\mathrm{yes} \\ $$

Commented by fantastic last updated on 14/Jun/25

no I mean is t_1 just a variable like x,y ?or it has speciality?

$${no}\:{I}\:{mean}\:\:{is}\:{t}_{\mathrm{1}} \:{just}\:{a}\:{variable}\:{like}\:{x},{y}\:?{or}\:{it}\:{has}\:{speciality}? \\ $$

Commented by hardmath last updated on 14/Jun/25

$$ \\ $$just like t1 (we can say variable)

Commented by fantastic last updated on 14/Jun/25

$${t}_{\mathrm{1}} ?? \\ $$

Answered by fantastic last updated on 14/Jun/25

I think it is 2^((2+2^((70−t_1 )/(10)) )) =2^((2+(2^7 /2^(t_1 /(10)) ))) =2^((((2^((t_1 +10)/(10)) +2^7 )/2^(t_1 /(10)) ))) =...[more complex] So I think the simpler form is 2^((2+2^((70−t_1 )/(10)) ) ) cause others are getting more complex

$${I}\:{think}\:{it}\:{is} \\ $$$$\mathrm{2}^{\left(\mathrm{2}+\mathrm{2}^{\frac{\mathrm{70}−{t}_{\mathrm{1}} }{\mathrm{10}}} \right)} =\mathrm{2}^{\left(\mathrm{2}+\frac{\mathrm{2}^{\mathrm{7}} }{\mathrm{2}^{\frac{{t}_{\mathrm{1}} }{\mathrm{10}}} }\right)} =\mathrm{2}^{\left(\frac{\mathrm{2}^{\frac{{t}_{\mathrm{1}} +\mathrm{10}}{\mathrm{10}}} +\mathrm{2}^{\mathrm{7}} }{\mathrm{2}^{\frac{{t}_{\mathrm{1}} }{\mathrm{10}}} }\right)} =…\left[{more}\:{complex}\right] \\ $$$${So}\:{I}\:{think}\:{the}\:{simpler}\:{form}\:{is}\:\mathrm{2}^{\left(\mathrm{2}+\mathrm{2}^{\frac{\mathrm{70}−{t}_{\mathrm{1}} }{\mathrm{10}}} \right)\:} \\ $$$${cause}\:{others}\:{are}\:{getting}\:{more}\:{complex} \\ $$$$ \\ $$

Commented by Frix last updated on 14/Jun/25

4^(1+64×2^(−(t_1 /(10))) ) =4^(1+((64)/( (2^t_1 )^(1/(10)) ))) Anyway not very simplify−able...

$$\mathrm{4}^{\mathrm{1}+\mathrm{64}×\mathrm{2}^{−\frac{{t}_{\mathrm{1}} }{\mathrm{10}}} } =\mathrm{4}^{\mathrm{1}+\frac{\mathrm{64}}{\:\sqrt[{\mathrm{10}}]{\mathrm{2}^{{t}_{\mathrm{1}} } }}} \\ $$$$\mathrm{Anyway}\:\mathrm{not}\:\mathrm{very}\:\mathrm{simplify}−\mathrm{able}… \\ $$

Commented by hardmath last updated on 14/Jun/25

2^((70−t_1 )/(10)) = 4 ∙ 4^((70−t_1 )/(10)) ⇒ t_1 = ?

$$\mathrm{2}^{\frac{\mathrm{70}−\boldsymbol{\mathrm{t}}_{\mathrm{1}} }{\mathrm{10}}} \:=\:\mathrm{4}\:\centerdot\:\mathrm{4}^{\frac{\mathrm{70}−\boldsymbol{\mathrm{t}}_{\mathrm{1}} }{\mathrm{10}}} \:\:\:\Rightarrow\:\:\:\mathrm{t}_{\mathrm{1}} \:=\:? \\ $$

Commented by Rasheed.Sindhi last updated on 14/Jun/25

The required is to simplify not to solve for t_1 The given is not an equation.

$${The}\:{required}\:{is}\:{to}\:{simplify} \\ $$$${not}\:{to}\:{solve}\:{for}\:{t}_{\mathrm{1}} \\ $$$${The}\:{given}\:{is}\:{not}\:{an}\:{equation}. \\ $$

Commented by Frix last updated on 14/Jun/25

$$\mathrm{Weirdness}\:\mathrm{taking}\:\mathrm{over}… \\ $$

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