# solve 2x^(-1/2)=8i think i know how but the exponent thing is confusing me so if someone could explain, that'd be awesome. :)

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Given: 2x^(-1/2) = 8

There are a few different ways you can solve this problem.

1. We can make the exponent positive by doing the following:

Multiply both sides of the quation by x^(1/2) so,

2x^(-1/2)*x^(1/2) = 8*x^(1/2)..... simplify

2 = 8x^(1/2) (because x^(-1/2) * x ^(1/2) = x^0 = 1)

Divide both sides by 8:

: 2/8 = 8x^(1/2)/8..... simplify

1/4 = x^(1/2)

To solve for x we need to square both sides of the equation (becuase x^(1/2) ^2 = x^(1/2) * x^(1/2) = x^1 = 1)

(1/4)^2 = x^(1/2)^2..... simplify

1/16 = x, so x = 1/16

A SECOND WAY: VERY similar to the first. (Just the beginning is different.)

2. A negative exponent can be made positive by making a fraction and moving it (along with its base) to the denominator (review rules of exponents).

So, 2x^(-1/2) = 8 is equivalent to 2/x^(1/2) = 8.

We can multiply both sides by x^(-1/2) to get it out of the denominator, moving it to the opposite side of the equation:

2/x^(1/2) * x^(1/2) = 8 * x^(1/2) ..... simplify

2 = 8x^(1/2)

Divide both sides by 8: 2/8 = 8x^(1/2)/8..... simplify

1/4 = x^(1/2)

To solve for x we need to square both sides of the equation (becuase x^(1/2) ^2 = x^(1/2) * x^(1/2) = x^1 = 1)

(1/4)^2 = x^(1/2)^2..... simplify

1/16 = x, so x = 1/16

To solve this equation:

2x^(-1/2)=8

We use the properties (a^b)^c=a^(b*c) and a^(-b)=(1/a)^b

Raise both the sides to the power ( - 2 )

=> [2x^(-1/2)]^(-2) = 8^(-2)

=> [2^(-2)*x^((-1/2)*(-2))] = (1/8)^(2)

=> (1/4)x = 1/64

=> x= 4/64

=>x=1/16

**Therefore we get the value of x as 1/16**