The value of the exponents in simple exponential form is
.
The mathematical operation of exponentiation, written as bⁿ, involves the base number (b) and the exponent (or power) number (n). The way to say this word is "b (elevated) to the (power of) n."
- Exponentiation corresponds to repeated base multiplication when n is a positive integer since bⁿ is the outcome of multiplying n bases. The exponent is often displayed to the right of the base as a subscript.
- The phrase "b to the nth power" or simply "b to the nth" is used to refer to bn. Other variations are "b (raised) to the power of n," "the nth power of b," and "b to the power of n" and "b to the nth power,"
The properties of exponents tell us that when the bases are equal then on multiplication the powers are added and on division the powers are subtracted.
![\sqrt[5]{5^y} \cdot(5^4)^3 = 5^{\frac{y+60}{5} }](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7B5%5Ey%7D%20%5Ccdot%285%5E4%29%5E3%20%3D%205%5E%7B%5Cfrac%7By%2B60%7D%7B5%7D%20%7D)
![\sqrt[5]{5^x} \cdot(5^4)^3 = 5^{\frac{x+60}{5} }](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7B5%5Ex%7D%20%5Ccdot%285%5E4%29%5E3%20%3D%205%5E%7B%5Cfrac%7Bx%2B60%7D%7B5%7D%20%7D)
Therefore the properties of exponents can be used to find the exponential solutions.
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Answer:
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Step-by-step explanation:
Answer:
The mean value theorem is valid if f(x) is continuous in the interval (0,3) and differentiable in the interval (0,3), the problem is that f(x)=2−|4x−2| is not differentiable in x = 1/2 because 4*1/2 - 2 = 0 and the function |x| is not differentiable in x = 0.
f'(x) = (-4)*(4x−2)/|4x−2|
f(3) = 2−|4*3−2| = 8
f(0) = 2−|4*0−2| = 0
Replacing in f'(c) = f(3)−f(0)/(3−0)
(-4)*(4c−2)/|4c−2| = (8 - 0)/3
(-4)*(4c−2)*3/8 = |4c−2|
-3/2*4c + 3/2*2 = |4c−2|
-6c + 3 = |4c−2|
That gives us two options
-6c + 3 = 4c−2
5 = 10c
1/2 = c
or
6c - 3 = 4c−2
-1 = -2c
1/2 = c
But f'(1/2) is not defined, therefore there is no value of c such that f(3)−f(0)=f'(c)(3−0).
Answer:
Step-by-step explanation:
Take a triangle ABC, in which AB=AC.
Construct AP bisector of angle A meeting BC at P.
In ∆ABP and ∆ACP
AP=AP[common]
AB=AC[given]
angle BAP=angle CAP[by construction]
Therefore, ∆ABP congurent ∆ACP[S.A.S]
This implies, angle ABP=angleACP[C.P.C.T]