Question

Rewrite the following expressions: 27^1/2 ⋅ 27^1/4
.(1 point)
Responses

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

2718
27 superscript Start Fraction 1 over 8 End Fraction baseline

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

2734

Answer 1

To simplify the expression \( 27^{1/2} \cdot 27^{1/4} \), you can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).

So,

\[
27^{1/2} \cdot 27^{1/4} = 27^{(1/2 + 1/4)}
\]

Now, let's find a common denominator to add \( 1/2 \) and \( 1/4 \):

\[
1/2 = 2/4
\]

Now, add:

\[
\frac{2}{4} + \frac{1}{4} = \frac{3}{4}
\]

So the expression simplifies to:

\[
27^{3/4}
\]

Now, we can write it in radical form:

\[
27^{3/4} = \sqrt[4]{27^3}
\]

Thus, the rewritten expression is:

\[
27^{3/4}
\]

This matches with:

**Response:** \( 27^{3/4} \)