Question

Using the properties of exponents, which expression is equivalent to 4^1/3⋅4^1/3
?(1 point)
Responses

43−−√
square root of 4 cubed end root

443
4 raised to the 4 thirds power

42−−√3
cube root of 4 squared

4^1/9

Answer 1

To simplify the expression \( 4^{1/3} \cdot 4^{1/3} \), you can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).

In your case:

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

Now let's analyze the options given:

1. **\( 4^{3/2} \)** - This is not equivalent to \( 4^{2/3} \).
2. **\( 4^{4/3} \)** - This is also not equivalent to \( 4^{2/3} \).
3. **\( 4^{2/3} \)** - This represents our simplified expression, but it's not listed directly as an option.
4. **\( \sqrt[3]{4^2} \)** - This expression is equivalent to \( 4^{2/3} \) because:
\[
\sqrt[3]{4^2} = 4^{2/3}
\]
5. **\( 4^{1/9} \)** - This is not equivalent to \( 4^{2/3} \).

Thus, based on the options provided, the expression that is equivalent to \( 4^{1/3} \cdot 4^{1/3} \) is:

**\( \sqrt[3]{4^2} \)** (or \( 4^{2/3} \)).