Because it is raised to the -1/4 you need to take the inverse of 1/16.
So it will become 16^1/4
Now from here you take 16 to the power in the numerator.
16^1 = 16
and then because the denominator is 4 you take the 4th root of 16
the 4th root of 16 = 2
Law of Exponents
This topic has expert replies
Source: Beat The GMAT — Problem Solving |
-
DanaJ
- Site Admin
- Posts: 2567
- Joined: Thu Jan 01, 2009 10:05 am
- Thanked: 712 times
- Followed by:550 members
- GMAT Score:770
Let's take everything step by step, then.
You have (1/16) raised to the power -1/4. We should tackle the minus first. That minus over there basically tells us that you should "flip" the fraction, turning 1/16 into 16/1 or 16. This is what a negative power means: just tun it over!
The general rule is that (a/b)^(-n) = (b/a)^n.
Now, let's see what we get: (1/16)^(-1/4) = 16^(1/4). Now, this 1/4 actually stands for the fourth degree root of 16, which will be 2, since 2^4 = 16. Following this rule, we get that sqrt(n) = n^(1/2). It's just another notation for roots.
The general rule over here is: a^(1/n) = the n-th degree root of a.
Let's take some more examples:
81^(1/4) = 3 (the fourth degree root), since 3^4 = 81
8^(1/3) = 2 (the third degree root), since 2^3 =8.
64^(1/6) = 2 (the sixth degree root), since 2^6 = 64.
You have (1/16) raised to the power -1/4. We should tackle the minus first. That minus over there basically tells us that you should "flip" the fraction, turning 1/16 into 16/1 or 16. This is what a negative power means: just tun it over!
The general rule is that (a/b)^(-n) = (b/a)^n.
Now, let's see what we get: (1/16)^(-1/4) = 16^(1/4). Now, this 1/4 actually stands for the fourth degree root of 16, which will be 2, since 2^4 = 16. Following this rule, we get that sqrt(n) = n^(1/2). It's just another notation for roots.
The general rule over here is: a^(1/n) = the n-th degree root of a.
Let's take some more examples:
81^(1/4) = 3 (the fourth degree root), since 3^4 = 81
8^(1/3) = 2 (the third degree root), since 2^3 =8.
64^(1/6) = 2 (the sixth degree root), since 2^6 = 64.
What if the problem was (1/16)^-3/4 what would I do with the 3DanaJ wrote:Let's take everything step by step, then.
You have (1/16) raised to the power -1/4. We should tackle the minus first. That minus over there basically tells us that you should "flip" the fraction, turning 1/16 into 16/1 or 16. This is what a negative power means: just tun it over!
The general rule is that (a/b)^(-n) = (b/a)^n.
Now, let's see what we get: (1/16)^(-1/4) = 16^(1/4). Now, this 1/4 actually stands for the fourth degree root of 16, which will be 2, since 2^4 = 16. Following this rule, we get that sqrt(n) = n^(1/2). It's just another notation for roots.
The general rule over here is: a^(1/n) = the n-th degree root of a.
Let's take some more examples:
81^(1/4) = 3 (the fourth degree root), since 3^4 = 81
8^(1/3) = 2 (the third degree root), since 2^3 =8.
64^(1/6) = 2 (the sixth degree root), since 2^6 = 64.
-
dmateer25
- Community Manager
- Posts: 1049
- Joined: Sun Apr 06, 2008 5:15 pm
- Location: Pittsburgh, PA
- Thanked: 113 times
- Followed by:27 members
- GMAT Score:710
(1/16)^-3/4vladmire wrote:What if the problem was (1/16)^-3/4 what would I do with the 3DanaJ wrote:Let's take everything step by step, then.
You have (1/16) raised to the power -1/4. We should tackle the minus first. That minus over there basically tells us that you should "flip" the fraction, turning 1/16 into 16/1 or 16. This is what a negative power means: just tun it over!
The general rule is that (a/b)^(-n) = (b/a)^n.
Now, let's see what we get: (1/16)^(-1/4) = 16^(1/4). Now, this 1/4 actually stands for the fourth degree root of 16, which will be 2, since 2^4 = 16. Following this rule, we get that sqrt(n) = n^(1/2). It's just another notation for roots.
The general rule over here is: a^(1/n) = the n-th degree root of a.
Let's take some more examples:
81^(1/4) = 3 (the fourth degree root), since 3^4 = 81
8^(1/3) = 2 (the third degree root), since 2^3 =8.
64^(1/6) = 2 (the sixth degree root), since 2^6 = 64.
because the 3 is negative you still take the inverse.
So it would become 16^3/4.
Now what you do is take the base 16 to 3rd power. and then you take the 4th root of this.
So it would be the 4th root of 16^3 which would equal 8.
-
chintudave
- Senior | Next Rank: 100 Posts
- Posts: 31
- Joined: Thu Sep 25, 2008 6:10 pm
- Thanked: 2 times
(1/16)^-1/4
= 16 ^ 1/4
i.e. 4th root of 16.
As others have said the answer is 4... however if this question shows up in DS... the options are 2, -2, 2i & -2i... so there is no single value to this problem.
= 16 ^ 1/4
i.e. 4th root of 16.
As others have said the answer is 4... however if this question shows up in DS... the options are 2, -2, 2i & -2i... so there is no single value to this problem.
