Respuesta :

lublana

Answer:

Choice (3) [tex]\left(2^2\right)^t[/tex] is correct.

Step-by-step explanation:


Given expression is [tex]\left(\frac{1}{2}\right)^{-2t}[/tex]

Now we need to simplify this and check which of the given choices best match with it.

[tex]\left(\frac{1}{2}\right)^{-2t}[/tex]

[tex]=\left(\frac{1}{2^1}\right)^{-2t}[/tex]

[tex]=\left(2^{-1}\right)^{-2t}[/tex] {using formula [tex]=\frac{1}{x^m}=x^{-m}[/tex]}

[tex]=\left(2^{-1}\right)^{-2t}[/tex] {using formula [tex]=\left(x^m\right)^n=x^{\left(m\cdot n\right)}[/tex]}

[tex]=2^{\left(-1\right)\left(-2t\right)}[/tex]

[tex]=2^{2t}[/tex]

[tex]=\left(2^2\right)^t[/tex] {using formula [tex]=\left(x^m\right)^n=x^{\left(m\cdot n\right)}[/tex]}

Hence choice (3) [tex]\left(2^2\right)^t[/tex] is correct.

alinakincsem

Answer:

The correct answer option is [tex](2^2)^t[/tex].

Step-by-step explanation:

We are given the following expression and we are to tell whether which of the given options is it equivalent to:

[tex](\frac{1}{2})^{-2t)[/tex]

If we look at the first option [tex]((\frac{1}{2} )^2)^t[/tex], the power is going to be positive here.

The second option will be equal to [tex]2^{-2t}[/tex] and not [tex](\frac{1}{2})^{-2t)[/tex].

While the third option is the correct one: [tex](2^2)^t[/tex].

When the 2 is shifted to the denominator, its power becomes negative and so it becomes equivalent to [tex](\frac{1}{2})^{-2t)[/tex].

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