Let's simplify the expression \( 2712 \cdot 2714 \).
We can express it in terms of powers of 27:
-
The expression can be rewritten as: \[ 2712 \cdot 2714 = 27^{12} \cdot 27^{14} \]
-
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 \( 2712 \cdot 2714 \):
-
27−−√4: \[ \sqrt[4]{27} = 27^{1/4} \] Does not match.
-
2734: \[ 27^{34} \text{ (which is } 27^{26} \text{ but no exponent is greater.)} \] Does not match.
-
27−−√3: \[ \sqrt[3]{27} = 27^{1/3} \] Does not match.
-
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.
19 answers