Question

Which of the following is equivalent to (1/2)^-2t

Answer 1

Answer:

Choice (3) $\left(2^2\right)^t$ is correct.

Step-by-step explanation:

Given expression is $\left(\frac{1}{2}\right)^{-2t}$

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

$\left(\frac{1}{2}\right)^{-2t}$

$=\left(\frac{1}{2^1}\right)^{-2t}$

$=\left(2^{-1}\right)^{-2t}$ {using formula $=\frac{1}{x^m}=x^{-m}$}

$=\left(2^{-1}\right)^{-2t}$ {using formula $=\left(x^m\right)^n=x^{\left(m\cdot n\right)}$}

$=2^{\left(-1\right)\left(-2t\right)}$

$=2^{2t}$

$=\left(2^2\right)^t$ {using formula $=\left(x^m\right)^n=x^{\left(m\cdot n\right)}$}

Hence choice (3) $\left(2^2\right)^t$ is correct.

Answer 2

Answer:

The correct answer option is $(2^2)^t$.

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:

$(\frac{1}{2})^{-2t)$

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

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

While the third option is the correct one: $(2^2)^t$.

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