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

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

Answer 2

B= Г2^5

Step-by-step explanation: