What is the division property of exponents?
1 answer:
<h3>Answer:</h3>
An exponent represents repeated multiplication. For example, ...
... x^3 = x·x·x
... x^2 = x·x
If we divide these, the x's in the denominator cancel an equal number in the numerator:
... (x·x·x)/(x·x) = x
If we represent the repeated multiplication using exponents, we can represent the cancellation by subtraction:
... (x^3)/(x^2) = x^(3-2) = x^1 = x
Once we have this idea in mind that division can be done by subtracting denominator exponents, we can use it regardless of the magnitude or sign of the exponents involved.
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Answer:
Volume of the similar sphere be 64 :343 .
Option (D) is correct.
Step-by-step explanation:
Formula
As given
The volumes of two similar spheres given that the ratio of their radii is 4:7 .
Let us assume that the x be the scalar multiple of the radi .
Radius of first sphere = 4x
Radius of second sphere = 7x
Putting the values in the formula
Thus
Therefore the ratio of the volume of the similar sphere be 64 :343 .
Option (D) is correct .
Base case: For , the left side is 2 and the right is
, so the base case holds.
Induction hypothesis: Assume the statement is true for , that is
We want to show that this implies truth for , that
The first terms on the left reduce according to the assumption above, and we can simplify the
-th term a bit:
so the statement is true for all .