Question

using the properties of exponents, which expression is equivalent to 4^1/3 x 4^1/3
A. √4^3
B. 4^4/3
C. 3√4^2
D. 4^1/9

Answer 1

To simplify the expression \(4^{1/3} \times 4^{1/3}\) using the properties of exponents, we can apply the rule that states \(a^m \times a^n = a^{m+n}\).

In this case, we have:

\[
4^{1/3} \times 4^{1/3} = 4^{(1/3) + (1/3)} = 4^{2/3}
\]

Now, we need to determine which of the provided options is equivalent to \(4^{2/3}\).

Let's evaluate each option:

A. \( \sqrt{4^3} = (4^3)^{1/2} = 4^{3/2} \)

B. \( 4^{4/3} \) (this does not match)

C. \( 3\sqrt{4^2} = 3 \cdot 4^{2/2} = 3 \cdot 4^1 = 3 \cdot 4 \) (this does not match)

D. \( 4^{1/9} \) (this does not match)

None of the options seem to be \( 4^{2/3} \).

Since \(4^{2/3} = (4^{1/3})^2\) and given that we have a mismatch with the options, we can confirm that the correct simplification \(4^{2/3}\) is not found among the answers provided.

Please check for any potential mistakes or inconsistencies in the options.