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Need Help Understanding Negative Exponents
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01 Aug 2025, 22:47
01 Aug 2025, 22:47
1
Hello,
Why does something like 2^(-3) equal 1/8? I’m having trouble grasping the concept of negative exponents. Any simple explanation?
Why does something like 2^(-3) equal 1/8? I’m having trouble grasping the concept of negative exponents. Any simple explanation?
Re: Need Help Understanding Negative Exponents
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04 Jul 2026, 12:02
04 Jul 2026, 12:02
1
It's probably easiest to just memorize that 2^{-3} = 1 / {2^3}
Alternatively, you can think of adding 1 to an exponent as iterated multiplication, starting from 2^0 = 1
2^1 = 2^0 * 2 = 2
2^2 = 2^0 * 2 * 2 = 4 etc.
Then since division is the inverse operation of multiplication, you can think of negative exponents as repeated division
2^{-1} = 2^0 / 2 = 1 / 2
2^{-2} = (2^0 / 2) / 2 = 1 / {2^2} etc.
Alternatively, you can think of adding 1 to an exponent as iterated multiplication, starting from 2^0 = 1
2^1 = 2^0 * 2 = 2
2^2 = 2^0 * 2 * 2 = 4 etc.
Then since division is the inverse operation of multiplication, you can think of negative exponents as repeated division
2^{-1} = 2^0 / 2 = 1 / 2
2^{-2} = (2^0 / 2) / 2 = 1 / {2^2} etc.
Re: Need Help Understanding Negative Exponents
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04 Jul 2026, 23:15
04 Jul 2026, 23:15
Expert Reply
More here sir
GRE Quant - Exponents and Roots Theory
https://gre.myprepclub.com/forum/gre-qu ... tml#p52033
GRE Quant - Exponents and Roots Theory
https://gre.myprepclub.com/forum/gre-qu ... tml#p52033
