Which of the following is an equivalent expression for 5 1/2/^3√125 when simplified using exponent properties.

1 answer

To simplify the expression \( 5 \frac{1}{2} / \sqrt[3]{125} \):

  1. First, convert the mixed number \( 5 \frac{1}{2} \) to an improper fraction: \[ 5 \frac{1}{2} = \frac{11}{2} \]

  2. Next, simplify \( \sqrt[3]{125} \): \[ 125 = 5^3 \quad \Rightarrow \quad \sqrt[3]{125} = \sqrt[3]{5^3} = 5 \]

  3. Now substitute back into the expression: \[ \frac{11}{2} / 5 \]

  4. Dividing by \( 5 \) is the same as multiplying by its reciprocal: \[ \frac{11}{2} \times \frac{1}{5} = \frac{11}{10} \]

Therefore, the simplified expression for \( 5 \frac{1}{2} / \sqrt[3]{125} \) is: \[ \frac{11}{10} \]

Thus, the equivalent expression is \( \frac{11}{10} \).