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

Question

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)