Answer:
Step-by-step explanation:
Since the denominator of each of those rational exponents is a 4, that means that the radical is a 4th root. The numerator of each exponent serves as the power on the given base. For example,
can be rewritten as
The little number that sits outside the radical, resting in the bend, is called the index. Our index is 4 (same as saying the 4th root). Put everything under the 4th root and let the numerator be the powers on each base:
which is written simpler as:
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Explanation:
Start with the point (-2,-4). Let's try to move it to (2, -9)
To do so, we need to shift down and to the right (in either order).
Specifically we shift 4 units to the right to go from x=-2 to x=4
Note how x=-2 moves to x+4 = -2+4 = 2
Also, we shift 5 units down. We have y = -4 turn into y = -9 as shown below
y ---> y-5 = -4-5 = -9
So the translation rule is
Let's see what happens when we apply the translation rule to (2,4)
which is the other endpoint of the blue segment. This shows that the translation rule works for (2,4) to move to (6,-1)
We do not apply any dilations. The red and blue segments are the same length because translations preserve distance. All we're effectively doing is moving the red segment to land on the blue segment. This means no vertical or horizontal stretches are done. The same can be said about compressions as well.