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If a^(-1/2)=x , where a gt 0 , what is a...

If `a^(-1/2)`=x , where a gt 0 , what is a in terms of x ?

A

`sqrtx`

B

`-sqrt2`

C

`1/x^2`

D

`-1/x^2`

Text Solution

AI Generated Solution

The correct Answer is:
To find \( a \) in terms of \( x \) given that \( a^{-1/2} = x \), we can follow these steps: ### Step 1: Rewrite the equation Start with the given equation: \[ a^{-1/2} = x \] ### Step 2: Eliminate the negative exponent To eliminate the negative exponent, we can rewrite the equation as: \[ \frac{1}{a^{1/2}} = x \] ### Step 3: Take the reciprocal Taking the reciprocal of both sides gives us: \[ a^{1/2} = \frac{1}{x} \] ### Step 4: Square both sides Now, to solve for \( a \), we square both sides: \[ (a^{1/2})^2 = \left(\frac{1}{x}\right)^2 \] This simplifies to: \[ a = \frac{1}{x^2} \] ### Final Answer Thus, we have expressed \( a \) in terms of \( x \): \[ a = \frac{1}{x^2} \]
To find \( a \) in terms of \( x \) given that \( a^{-1/2} = x \), we can follow these steps: ### Step 1: Rewrite the equation Start with the given equation: \[ a^{-1/2} = x \] ...
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