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9 solutions
why answer is 512? the power to power property is that 2^3*2=2^6=64 because in question small brackets are not appropriately placed,if i place small brackets here (2^3)^2=8^2=64.so how do we arrive at a definite solution.
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Power is given to the power not the base
When the brackets are not appropriately placed, how do we arrive at a definite solution?
(a^m)^n =a^mn as per maths rules like BEDMAS
Ugh...a syntax problem. Good to know, but not much fun.
To all of the other comments:
What you are saying is only true when you have parentheses around the base and the first exponent, like this: ( 2 3 ) 2 . In this case, the exponents are multiplied, but without the parenteses, you just calculate exponents from the top downwards. In this case, the 3 2 first, which equals 9, and then do 2 9 , which gives you 512.
This happens whenever you do not place parentheses. Hope this helps!
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is not true, we can raise a power to a power, and that is 3 per 2 an then: 2^6 equals to 64.... This is called the power of a power property and says that to find a power of a power you just have to multiply the exponents.
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the exponential operator is right associative. Meaning you must evaluate powers on the right first. So, 2^3^2 is 512 not 64. It would've been 64 only when the question was (2^3)^2
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Equate to x and take sqrt of both sides gives you sqrt of 8=sqrt x then x is 64
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@Zakaria Salameh – 2 3 2 = 2 ( 3 2 )
So 2 3 2 = 2 9 = 2 3
2 3 2 = ( 2 3 ) ⋅ ( 2 3 )
So, 2 3 2 = 2 ( 3 2 ) = 2 9 = 5 1 2
in what case we multiplies the powers?
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If it was given, (2^3)^2. We could multiply the powers and write 2^6 = 64
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The concept behind these problems is called tetration. So it's 512. Sometimes I hate being limited to writing "flat." 2^3^2 looks so confusing when we write it. But we see the 2nd power affects the 3 not 2^3.
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@A Former Brilliant Member – Thank you for mentioning tetration. That gave me something to search to look for more info. Although it seems like tetration really implies iterated exponents, the information I found still did a good job of explaining exponents of exponents as well.
@A Former Brilliant Member – 64 is right. because when a power gets a power they multiplies. in this case its 3*2=6 and then 2^6 = 64
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@Harsh Shah – Nope. A power to a power is different from (2^3)^2. A power to a power is not the same as a base to a power raised to a power. I'm talking about 2^(3^2) while you're talking about (2^3)^2. They're different. Plus as you can see in the original problem, the 2 is above and to the right of the 3. That's why the two effects the three before it affects the 2 to the 3rd.
Google tetration.
oh...again it is game of bracket.... thanks subhajit
if there was any bracket mentioned :)
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I'm pretty much sure that when we don't have brackets powers are multiplied !!
Brackets should be there
2 3 2 = ?
3 2 = 9
2 9 = 5 1 2
2^(3^2)=2^9=512 is that right ?
Yup, apparently, that's how other people did it.
you need parentheses to differentiate the order as far as I am concerned
we have to go from the top to the bottom. so 2^{3^}^{2} = 2^{3^{2}} = 2^{9} = 512
3x2=6 2x2x2x2x2x2=512 .512 is the correct answer.
Tower rule, 2^3^2 = 2^(3^2) = 2^9 = 512
2^3^2 = 2 ^9 = 512 because the tower rule says that we must work. from the top to the bottom
well from what i've learned its from the left to the right. that would've been 64. weird
Perform the exponent's power first,then solve the base expression.
By the Tower Rule , 2 3 2 = 2 ( 3 2 ) = 2 9 = 5 1 2