Answer:
![\sqrt[n]{x}=x^{\frac{1}{n}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%7D%3Dx%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D)
Step-by-step explanation:
The index of a radical is the denominator of a fractional exponent, and vice versa. If you think about the rules of exponents, you know this must be so.
For example, consider the cube root:
![\sqrt[3]{x}\cdot \sqrt[3]{x}\cdot \sqrt[3]{x}=(\sqrt[3]{x})^3=x\\\\(x^{\frac{1}{3}})^3=x^{\frac{3}{3}}=x^1=x](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%7D%5Ccdot%20%5Csqrt%5B3%5D%7Bx%7D%5Ccdot%20%5Csqrt%5B3%5D%7Bx%7D%3D%28%5Csqrt%5B3%5D%7Bx%7D%29%5E3%3Dx%5C%5C%5C%5C%28x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%29%5E3%3Dx%5E%7B%5Cfrac%7B3%7D%7B3%7D%7D%3Dx%5E1%3Dx)
That is ...
![\sqrt[3]{x}=x^{\frac{1}{3}} \quad\text{radical index = fraction denominator}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%7D%3Dx%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%20%5Cquad%5Ctext%7Bradical%20index%20%3D%20fraction%20denominator%7D)
Answer:
two coins are flipped:
- if dime land heads and nickel land heads then Allan wins
- if dime land heads and nickel land tail then Beth wins
- if dime land tail and nickel land heads then Carlos wins
- if dime land tail and nickel land tail then Denesha wins
Step-by-step explanation:
The method described above is fair since the probability of each case is 0.25.
If the two coins are flipped:
- The probability dime land head is 0.5
- The probability dime land tail is 0.5
- The probability nickel land head is 0.5
- The probability nickel land tail is 0.5
Then the probability dime land heads and nickel land heads is 0.5 × 0.5 = 0.25.
The other four cases are calculated similarly and their probability is also 0.25
10 to the power of 3 would be 1000.
2 to the power of 3 would be 8.
1000 x 8 = 8000
I hope this helped you <3
Answer:
Sorry I made a mistake here is a picture of the answer. I hope this helps.
