Question

Using the exponent properties, which of the following expressions is equivalent to 2exponent3/2 times 2- exponent1/2

Answer 1

To simplify the expression \( 2^{3/2} \times 2^{-1/2} \) using the properties of exponents, you can apply the rule that states \( a^m \times a^n = a^{m+n} \).

Here, you have:

\[
2^{3/2} \times 2^{-1/2} = 2^{(3/2) + (-1/2)}
\]

Now, we can add the exponents:

\[
3/2 - 1/2 = \frac{3 - 1}{2} = \frac{2}{2} = 1
\]

Therefore, the expression simplifies to:

\[
2^{1} = 2
\]

So, the original expression \( 2^{3/2} \times 2^{-1/2} \) is equivalent to \( 2 \).