What number raised to the -2 exponent would equal 1/4?

Answer 1

2

Answer 2

Actually there are two numbers that equal 1/4 when raised to the -2 power. The solution is laid out below.

x^(-2) = 1/4
1/x^(2) = 1/4
x^(2) = 4
x = 2 or -2

The first step is simply the word problem converted into an equation. The second step uses the property that a negative exponent term is equivalent to its inverse without the negative exponent. And then the algebra is straight forward from there. To check this solution:

2^(-2) = 1/4
(-2)^(-2) = 1/4

I hope that shows you not only the answer, but also how to do similar problems in the future.

Answer 3

2

Answer 4

x~-2=1/4 i think its
x=2 or
=-2
coz x raised to -2 is also equal to 1/x to raised 2
then you square root it at the both sides so 4 square rooted is +2 or -2

Answer 5

2^-2 = 1/4
3^-2 = 1/9
4^-2 = 1/16

see the pattern....

Negative exponents mean that instead of multiplying that many of the basetogether, you divide.

The way most people think of negative exponents is "put it in the bottom of the fraction."

Answer 6

x^-2 = 1/4

Well, when you raise to a negative exponent, it basically flips the fraction.

So, x = 2.

Answer 7

actually i m confused what do u wanna ask....

case 1: if u ask this (x)^(-2)=(1/4) than what is x?
case 2: if u ask this (-2)^x=1/4 than what is x?

so i answer both:

answer to case 1: x =2,
coz (2)^(-2)= 4^(-1)=1/4

answer to case 2: taking log on both sides, we get
=> (-2)^x=1/4
=> (-2)^x=(2)^(-2)
=> x log (-2)=(-2) log (2)
=> x = [ (-2) log (2) ] / [log(-2)]

now log(-2) can be calculated using complex nos., there is a direct formula for it, but i don't remember it as in m outta touch....so find it yourself

Answer 8

16 to the power -2 Equals a quarter.

Answer 9

I think it is 2.

Answer 10

5

oh wait...I was wrong...it is 2