Rewrite the following expressions: 2712⋅2714

Question

.(1 point)
Responses

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

2734
27 superscript Start Fraction 3 over 4 End Fraction baseline

2718
27 superscript Start Fraction 1 over 8 End Fraction baseline

27−−√4

Answer 1

To rewrite the expression \( 2712 \cdot 2714 \), we can simplify it using the properties of exponents.

The base \( 27 \) can be expressed as \( 27^{12} \cdot 27^{14} = 27^{12 + 14} = 27^{26} \).

Among the responses you provided, it seems none directly represent this result. However, we can express \( 27^{26} \) using other forms:

1. \( 27^{26} \) can be broken down further:
   • It is equivalent to \( (27^3)^{8} \), or \( 27^{3} \) raised to the power of \( 8 \), which could be expressed in the form \( 27^{\frac{3}{4}} \).
   • If we focus on the roots, \( 27^{\frac{1}{8}} \) could also represent a manipulation involving eighth roots.

If you need specific forms from the provided ones or any other forms of calculations, please clarify what you're looking for, and I’d be glad to assist!