what is the simplified version of 4 1/2

Answer 1

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 2

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

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.