Fraction raised to a negative exponent
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Is (1/5) ^ -2 = 25? Is it correct to flip the fraction (1/5 becomes 5) then square 5 =25?
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- ceilidh.erickson
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Yes, "flipping the fraction" is the same as taking the reciprocal. The reciprocal of 1/5 is 5, so (1/5)^(-2) = 5^2.Lookingfor700GMAT wrote:Is (1/5) ^ -2 = 25? Is it correct to flip the fraction (1/5 becomes 5) then square 5 =25?
Ceilidh Erickson
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Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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- Brent@GMATPrepNow
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in general, (x/y)^(-n) = (y/x)^n
So, for example, (2/3)^(-5) = (3/2)^5
Cheers,
Brent
So, for example, (2/3)^(-5) = (3/2)^5
Cheers,
Brent
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We could prove that easily enough too!
(1/x)�² = x²
is the same as
1 = x�² * x²
is the same as
1 = x�
which is true!
(1/x)�² = x²
is the same as
1 = x�² * x²
is the same as
1 = x�
which is true!
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Yes, you can do that. Another way to think about it is treat 1/5 as 5^-1.Lookingfor700GMAT wrote:Is (1/5) ^ -2 = 25? Is it correct to flip the fraction (1/5 becomes 5) then square 5 =25?
(1/5)^-2
(5^-1)^-2
5^(-1*-2)
5^2
25