Question

Generate an equivalent expression to 13^6⋅13^−1/2.(1 point)
Responses

1133
Start Fraction 1 over 13 cubed End Fraction

13−3
13 superscript negative 3 baseline

13112
13 superscript Start Fraction 11 over 2 End Fraction baseline

133
13 cubed

Answer 1

To simplify the expression \( 13^6 \cdot 13^{-1/2} \), we can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).

1. Combine the exponents:
\[
13^6 \cdot 13^{-1/2} = 13^{6 - 1/2}
\]

2. Convert \( 6 \) into a fraction with a denominator of \( 2 \):
\[
6 = \frac{12}{2}
\]

3. Now, combine the fractions:
\[
6 - \frac{1}{2} = \frac{12}{2} - \frac{1}{2} = \frac{11}{2}
\]

4. Therefore, the expression becomes:
\[
13^{11/2}
\]

Thus, the equivalent expression to \( 13^6 \cdot 13^{-1/2} \) is \( 13^{11/2} \).

The correct response is:
**13112** (13 superscript Start Fraction 11 over 2 End Fraction baseline)