Equation in exponents

Algebra Level 2

$\Large \color{#20A900}{(6x)^6=6^{2^3}}$

Find the positive value of $x$ that satisfy the equation above.

1

\sqrt[3]{6}

\sqrt{6}

None of the given.

\sqrt[6]{6}

2 solutions

Abhishek Sharma
May 12, 2015

${ \left( 6x \right) }^{ 6 }={ 6 }^{ { 2 }^{ 3 } }$ ${ 6 }^{ 6 }\times { x }^{ 6 }={ 6 }^{ { 2 }^{ 3 } }$ $x^{ 6 }={ 6 }^{ { 2 }^{ 3 }-6 }$ $x^{ 6 }={ 6 }^{ { 2 } }$ $x={ 6 }^{ { \frac { 1 }{ 3 } } }$ $x=\sqrt [ 3 ]{ 6 }$

I have a question please any one help me to find out the correct answer . I put the two forms of the math on the google then I get two result by two forms

(6^2)^3 = 46656;
6^2^3 =1679616

I can't understand . please give me suggestion for this problem. Thanks

Vubon Roy - 6 years ago

When you use 6^2^3, you must do like this.
6^2^3 = 6^8 And with a (), you must do like this.
(6^2)^3= 36 ^3

Alviando Hendriawan - 6 years ago

Well the point is, you must do the calculation from top to bottom if there are no parentheses

Alviando Hendriawan - 6 years ago

Can you explain me (6^2)^3= 36 ^3 or 6^6 this ?? why this like it please

Vubon Roy - 6 years ago

@Vubon Roy – if there is parentheses, you need to solved the one that is inside them. Okay?

Alviando Hendriawan - 6 years ago

so pardon for my derange but this is very interestingly ,because i have got one email with this exercise :

Which is larger

A = 4^3^2 OR B = 2^3^4 ?

and there are 3 answers :

B
A
equal

so because the rule of exponents say that x^a^b = x^(a b) so than A = 4^6 = 2^2^6 = 2^12 and B = 2^(3 4) = 2^12
so result that the right answer is 3. so equal
than in case of this exercise was accepted like right answer that A EQUAL B so than 4^3^2 = 2^2^3^2 = 2^(2 3 2) = 2^12 and than 2^3^4 = 2^(3*4) = 2^12 so

PLEASE GIVE one explication why in the case of above math. exercise not is the right answer x=1 ? - in case of same exercises we can using different math. rules so how is this possible ? - wait your reply ,thank you in advance !

András János Gábor - 5 years, 11 months ago

The answers are here .

Pi Han Goh - 5 years, 11 months ago

thank you for your reply but i think not can be accepted because look please than in case of example exercise what was : what is larger : A = 2^3^4 or B = 4^3^2 so the correct answer is EQUAL, than please try explain me why not we get A = 2^81 and B = 4^9 and i think that in this case A not will be equal B never - so do you can explain me this please ? - thank you in advance - András

András János Gábor - 5 years, 11 months ago

@András János Gábor – It's a common misconception to solve the exponents from the left to right. For example,

$2^{4^3} = 2^{(4^3)} = 2^{64} = 18446744073709551616$ is correct while
$2^{4^3} = {(2^4)}^3 = 16^3 = 4096$ is wrong..

Pi Han Goh - 5 years, 11 months ago

@Pi Han Goh –

thank you very much Dear ! so one question again please ,these mean that what i have learned about rule of exponents in my schools till 1991 ,inclusive in University 2 years - so this mean that today ALL these rules have forget their availability ? for example one rule was that (x^a)^b = x^(a*b) - so how you have wrote above in your example result that this rule today not is right - or i not understand your example correct,right ? wait your reply - thank you - András

András János Gábor - 5 years, 11 months ago

@András János Gábor – Notice the difference in the way I write $2^{4^3}$ and $(2^4)^3$ . You should always do the arithmetic inside the parenthesis first.

Here's another example, $2^{2^{2^{2}}} = 2^{2^{4}} = 2^{{16}} = 65536$ is correct. But $2^{2^{2^{2}}} = ((2^2)^2)^2 = ((4^2)^2 = 16^2 = 256$ is wrong.

To put it short, $a^{b^c} = a^{(b^c)}$ is correct while $a^{b^c} = (a^b)^c$ is wrong.

Pi Han Goh - 5 years, 11 months ago

@Pi Han Goh – thank you very much - good luck - András

András János Gábor - 5 years, 11 months ago

Aamir Waheed
May 20, 2015

Just adding a simplification process in Abhishek Sharma's solution: ${ \left( 6x \right) }^{ 6 }={ 6 }^{ { 2 }^{ 3 } }$ ${ 6 }^{ 6 }\times { x }^{ 6 }={ 6 }^{ 8 }$ $x^{ 6 }={ 6 }^{ 8-6 }$ $x^{ 6 }={ 6 }^{ { 2 } }$ $x={ 6 }^{ { \frac { 1 }{ 3 } } }$ $x=\sqrt [ 3 ]{ 6 }$

1 seems to be right answer. (6x)^6=6^2^3 (6x)^6=6^6 (6x)=6 x=1

Hiren Jobanputra - 6 years ago

Wrong. $6^{2^3} = 6^{(2^3)} = 6^8$ is correct, while $6^{2^3} = (6^2)^3 = 6^{2 \cdot 3} = 6^6$ is wrong.

Pi Han Goh - 6 years ago

i dont think so..... the correct option should be 1.... 6^2^3=6^6

Yash Parmar - 6 years ago

ok. Thanks. now i solved my query.

Hiren Jobanputra - 6 years ago

Interesting, what is wrong with thinking this way: (6^2) (6^2) (6^2)=6^6?

Ruben Garcia Berasategui - 6 years ago

@Ruben Garcia Berasategui – You need to perform the operation from the top to the bottom.

Pi Han Goh - 6 years ago

@Ruben Garcia Berasategui – By convention the order of calculation is top-down, not bottom-up. To modify the order of calculation use parentheses.

Aamir Waheed - 6 years ago

@Aamir Waheed – Thanks for the clarification guys. I understand now.

Ruben Garcia Berasategui - 6 years ago

Equation in exponents

2 solutions

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