The correct answer is 2.
To solve this problem using exponent properties, we can rewrite (√2)^3 as (√2)^(2/2) and rewrite 2^(-1/2) as 2^(1/2)^(-1).
Then, (√2)^3⋅2^(-1/2) becomes (√2)^(2/2) * 2^(1/2)^(-1).
By applying the exponent property (a^m * a^n = a^(m+n)), this expression simplifies to (√2)^(2/2 + 1/2 * -1).
Since 2/2 + 1/2 * -1 simplifies to 1, we have (√2)^1.
Finally, any number raised to the power of 1 is equal to the number itself, so (√2)^1 is equal to √2.
Therefore, the equivalent expression is √2, option 2.
Using the exponent properties, which of the following expressions is equivalent to (√2)^3⋅2^−1/2?(1 point)
Responses
2^2
√2
261/2
2
1 answer