Question

what is the simplified version of 4 1/2

Answer 1

what rational number could be used as an exponent to rewrite 5√20

Answer 2

The mixed number \( 4 \frac{1}{2} \) can be converted to an improper fraction. To do this, you multiply the whole number by the denominator and then add the numerator.

1. Multiply the whole number \( 4 \) by the denominator \( 2 \):
\( 4 \times 2 = 8 \)

2. Add the numerator \( 1 \):
\( 8 + 1 = 9 \)

3. Place that sum over the original denominator:
\( \frac{9}{2} \)

So, the simplified version of \( 4 \frac{1}{2} \) is \( \frac{9}{2} \).

Answer 3

To rewrite \( 5\sqrt{20} \) with a rational number as an exponent, we can first express \( \sqrt{20} \) in a simpler form.

1. **Simplify \( \sqrt{20} \)**:
- We know that \( 20 = 4 \times 5 \).
- So, \( \sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5} \).

2. **Now express \( 5\sqrt{20} \)**:
- Substituting back, we get:
\[
5\sqrt{20} = 5(2\sqrt{5}) = 10\sqrt{5}.
\]

3. **Rewrite \( \sqrt{5} \)**:
- The square root can be expressed as an exponent:
\[
\sqrt{5} = 5^{1/2}.
\]

4. **Combine everything**:
- Using this, we rewrite \( 10\sqrt{5} \):
\[
10\sqrt{5} = 10 \cdot 5^{1/2}.
\]

5. **Express 10 as a power of 5** (if necessary):
- If you want to express \( 10 \) in terms of the base \( 5 \), note that \( 10 \) can be rewritten in scientific notation:
\[
10 = 5^1 \cdot 2^1.
\]
- Thus, you can say:
\[
10\sqrt{5} = 2 \cdot 5^1 \cdot 5^{1/2} = 2 \cdot 5^{1 + 1/2} = 2 \cdot 5^{3/2}.
\]

In conclusion, \( 5\sqrt{20} \) can be rewritten as \( 2 \cdot 5^{3/2} \) using rational exponents.