PLEASE HELP!!!! Rewrite the rational exponent as a radical by extending the properties of integer exponents. 2 to the 3 over 4 p
ower, all over 2 to the 1 over 2 power
1 answer:
Whenever you have a number raised to a fraction, you can easily convert it to radical form.
The bottom half of the fraction (or the denominator) tells you what root you are finding. For example, if you have a 2 for the denominator, you are finding the square root (2). And if you have a 3, you are finding the cube root (3).
The top half of the fraction (or the numerator) tells you to what power the number inside the radical is being raised. For example, if you have a 2 for the numerator, you are squaring the number. If you have a 3, you are raising it to the third power.
In your case, you have 2 raised to the 3/4 power divided by 2 raised to the 1/2 power. Let's start with the top half.
2 raised to the 3/4 power - The denominator is a 4, so you are finding the fourth root of the 2. And since you have a 3 for the numerator, the 2 is raised to the 3rd power. So, the top expression is simplified as the fourth root of 2 cubed.
Now the bottom half. 2 raised to the 1/2 power - the denominator is 2, so you are finding the square root of the 2. And with one being the numerator, you don't have to worry - the two stays the same. So, it is simplified as the square root of two.
I've attached a picture of the expression so you can better understand what I mean. I hope this helps. :D
The bottom half of the fraction (or the denominator) tells you what root you are finding. For example, if you have a 2 for the denominator, you are finding the square root (2). And if you have a 3, you are finding the cube root (3).
The top half of the fraction (or the numerator) tells you to what power the number inside the radical is being raised. For example, if you have a 2 for the numerator, you are squaring the number. If you have a 3, you are raising it to the third power.
In your case, you have 2 raised to the 3/4 power divided by 2 raised to the 1/2 power. Let's start with the top half.
2 raised to the 3/4 power - The denominator is a 4, so you are finding the fourth root of the 2. And since you have a 3 for the numerator, the 2 is raised to the 3rd power. So, the top expression is simplified as the fourth root of 2 cubed.
Now the bottom half. 2 raised to the 1/2 power - the denominator is 2, so you are finding the square root of the 2. And with one being the numerator, you don't have to worry - the two stays the same. So, it is simplified as the square root of two.
I've attached a picture of the expression so you can better understand what I mean. I hope this helps. :D
You might be interested in