Rewrite the following expressions: 2712⋅2714 .(1 point) Responses 27−−√4 root index 4 Start Root 27 End Root 27−−√3 root index 3 Start Root 27 End Root 2734 27 superscript Start Fraction 3 over 4 End Fraction baseline 2718

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1 month ago

The expression \( 2712 \cdot 2714 \) can be rewritten using properties of exponents.

1. **Using Exponent Properties**:
\[
2712 \cdot 2714 = 27^{12} \cdot 27^{14} = 27^{12 + 14} = 27^{26}
\]

2. **Using Root Properties**:
The expression \( 27^{12} \cdot 27^{14} \) can also be expressed in radical form:
\[
27^{26} = \sqrt[4]{27^4} = \sqrt[3]{27^3} = 27^{3 \cdot \frac{26}{3}} = 27^{\frac{78}{3}} = 27^{26}
\]

So, combining these, we can write:

\[
2712 \cdot 2714 = 27^{26}
\]

This is a simplified and rewritten form of the expression \( 2712 \cdot 2714 \).