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09 Dec 2023, 03:36
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\(a = -0.3\) and we need to find the relationship between a, \(a^2\) and \(a^3\)
Let's solve the problem using two methods:
Method 1: Substitution
a = -0.3
\(a^2\) = \((-0.3)^2\) = 0.09
\(a^3\) = \((-0.3)^3\) = -0.027
=> a < \(a^3\) < \(a^2\)
So, Answer will be B
Method 2: Logic
Now \(a^2\) will be positive and will be greater than a and \(a^3\)
As a is a negative fraction between -1 and 0
=> \(a^3\) will become a smaller negative number and will be greater than a
\(a^3\) = -0.027 > -0.3
=> a < \(a^3\) < \(a^2\)
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Exponents
Let's solve the problem using two methods:
Method 1: Substitution
a = -0.3
\(a^2\) = \((-0.3)^2\) = 0.09
\(a^3\) = \((-0.3)^3\) = -0.027
=> a < \(a^3\) < \(a^2\)
So, Answer will be B
Method 2: Logic
Now \(a^2\) will be positive and will be greater than a and \(a^3\)
As a is a negative fraction between -1 and 0
=> \(a^3\) will become a smaller negative number and will be greater than a
\(a^3\) = -0.027 > -0.3
=> a < \(a^3\) < \(a^2\)
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Exponents
22 Jun 2025, 20:00
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Bunuel, i still don't understand how -0.3 is lesser than -0.027, isn't the magnitude of 0.027 is lesser than 0.3?? could you please elaborate...
EMPOWERgmatRichC
22 Jun 2025, 20:06
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Try to put the values on number line
-0.3 will be at the leftmost part
Then will come -0.027 which is a^3 in left of -0.3
Then will come 0.09 ie a^2
So a<a^3<a^2
-0.3 will be at the leftmost part
Then will come -0.027 which is a^3 in left of -0.3
Then will come 0.09 ie a^2
So a<a^3<a^2
SwethaReddyL
