Rewrite the following expressions: 2712⋅2714 .(1 point)

Responses

27−−√4
root index 4 Start Root 27 End Root

2734
27 superscript Start Fraction 3 over 4 End Fraction baseline

27−−√3
root index 3 Start Root 27 End Root

2718

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

Let's simplify the expression \( 2712 \cdot 2714 \).

We can express it in terms of powers of 27:

1. The expression can be rewritten as:
\[
2712 \cdot 2714 = 27^{12} \cdot 27^{14}
\]

2. Using the property of exponents \( a^m \cdot a^n = a^{m+n} \), we can combine the exponents:
\[
27^{12 + 14} = 27^{26}
\]

Thus, the expression \( 2712 \cdot 2714 \) can be rewritten as \( 27^{26} \) or as one of the given options if it fits.

However, it seems like the options provided (27−−√4, 2734, 27−−√3, 2718) don't directly match \( 27^{26} \).

Let's evaluate the responses individually against \( 2712 \cdot 2714 \):

1. **27−−√4**:
\[
\sqrt[4]{27} = 27^{1/4}
\]
Does not match.

2. **2734**:
\[
27^{34} \text{ (which is } 27^{26} \text{ but no exponent is greater.)}
\]
Does not match.

3. **27−−√3**:
\[
\sqrt[3]{27} = 27^{1/3}
\]
Does not match.

4. **2718**:
\[
27^{18} \text{ (which is lower than } 27^{26}.)
\]
Does not match.

It seems that none of the provided responses are equivalent to the simplified expression \( 27^{26} \).

If you'd like to rewrite \( 2712 \cdot 2714 \) solely in those provided forms, please clarify if I can provide an alternative form or interpret the values in a different way.