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Find the value of P such that 2 ^p sqrt 4 x 1/4

Find The Value Of P Such That 2 P Sqrt 4 X 14 class=

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MathTutors

Answer: p=-1

Step-by-step explanation:

To find the value of p, we can manipulate the right side so that it looks like the left.

We know that [tex]\sqrt{4}=2[/tex]. Therefore, it can be written as 2¹.

[tex]\frac{1}{4}[/tex] is the same as [tex]\frac{1}{2^2 }[/tex] because 2²=4. To make it not a fraction, we can flip it and change the exponent. [tex]\frac{1}{4}=2^-^2[/tex]

Now, we can put them together.

[tex]2^p=2^1*2^-^2[/tex]         [multiply]

[tex]2^p=2^-^1[/tex]

Now, we know that p=-1.

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