Question

Which expression is equivalent to (2^1/2 x 2^3/4)^2

a. 4√2^3
b. √2^5
c. 4√4^3
d. √4^5
need correct answer asap

Answer 1

B= Г2^5

Explanation:

Answer 2

We basically use rules of indices or exponents on this one and simplify.

`({2^(1/2)*2^(3/4))^(2)`

When we have same base to a power multiplied together, we add the exponents. So we have,

`(2^(1/2+3/4))^(2)\\(2^(5/4))^(2) \\`

When we have power raised to a power, we multiply the powers. So we have,

`2^(10/4)`

Simplifying the fraction, we have

`2^(5/2)`. Since the answer choices have a square root sign, this can be changed to include square roots and powers using the formula,

`\sqrt[n]{x^(m)} =  x^(m/n)`.

Now we can write
`2^(5/2)` as
`\sqrt[2]{2^(5)}`.

Just omit the 2 outside the square root sign as we don't need to write that due to convention. So we have
`\sqrt{2^(5)}`. This is answer choice (B).

ANSWER: B