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kodGreya [7K]
2 years ago
14

In Exercise,Use properties of exponents to simplyfy the expression. (e2/3)(e3)

Mathematics
1 answer:
Wittaler [7]2 years ago
8 0

Answer: e^{\frac{11}{3}}

Step-by-step explanation:

According to the Multiplication property of exponents : a^m\cdot {a^n}=a^{m+n}

For example : 2^7\cdot 2^5= 2^{7-5}=2^2

Let's take one more example , a^{-11}\cdot a^{1}=a^{-11+1}=a^{-10}

The given expression : (e^{\frac{2}{3}})(e^3)

By Multiplication property of exponents , we have

(e^{\frac{2}{3}})(e^3)=e^{\frac{2}{3}+3}

=e^{\frac{2+3(3)}{3}}=e^{\frac{2+9}{3}}

=e^{\frac{11}{3}}

Hence, the simplified expression is e^{\frac{11}{3}} .

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find the number 15 balls consisting of 5 black, 5 blue nd 5 white balls from a box which has 6 black, 7 blue and 8 white balls (
AleksAgata [21]

Answer:

Step-by-step explanation:

A bag contains 4 blue, 5 white, and 6 green balls. ... There are 5 red and 15 black balls in a box, two are picked up at random

4 0
3 years ago
I need the answers for 5 and 6 please and make sure they are accurate , thank you :)
velikii [3]

Answer:

5. 6+6i

6. -2+(6\sqrt{3})i

Step-by-step explanation:

well, u just need to calculate

7 0
2 years ago
Can someone help me with this? I need to find the points of discontinuity/limits for each of these. I think one point is 4, but
Debora [2.8K]
The answers are shown in the attached image

-------------------------------------------------------------------------

Explanation:

Set the denominator x^4-8x^3+16x^2 equal to zero and solve for x

x^4-8x^3+16x^2 = 0
x^2(x^2-8x+16) = 0
x^2(x-4)^2 = 0
x^2 = 0 or (x-4)^2 = 0
x = 0 or x-4 = 0
x = 0 or x = 4

The x values 0 and 4 make the denominator zero

These x values lead to asymptote discontinuities because the numerator 8x-24 = 8(x-3) has no common factors which cancel with the denominator factors.

There are two vertical asymptotes

Let's see what happens when we plug in a value to the left of x = 0, say x = -1, we'd get
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(-1) = (8(-1)-24)/((-1)^4-8(-1)^3+16(-1)^2)
f(-1) = -1.28
So as x gets closer and closer to x = 0 from the left side, the f(x) is heading to negative infinity

Now plug in some value to the right of x = 0. I'm going to pick x = 1
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(1) = (8(1)-24)/((1)^4-8(1)^3+16(1)^2)
f(1) = -1.78 (approximate)
So as x gets closer and closer to x = 0 from the right side, the f(x) is heading to negative infinity

Overall, as x approaches 0 from either the left or right side of x = 0, the y value is heading off to negative infinity

---------------------

Repeat for values to the left and right of x = 4
We can't use x = 1 as it turns out that x = 3 is a root
But we can use something like x = 3.5 to find that...
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(3.5) = (8(3.5)-24)/((3.5)^4-8(3.5)^3+16(3.5)^2)
f(3.5) = 1.31 approx
So as x gets closer to x = 4 from the left, y is getting closer to positive infinity

Plug in x = 5 to find that
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(5) = (8(5)-24)/((5)^4-8(5)^3+16(5)^2)
f(5) = 0.64
which has the same behavior as the left side

So overall, as we approach x = 4, the y value is heading off to positive infinity

Again everything is summarized in the image attachment

Note: you could make a table of more values but they would effectively say what has already been said. It would be redundant busy work. However, its always good practice for function evaluation. 

6 0
2 years ago
What is the quotient (2x3 − 15x2 − 10x + 16) ÷ (x − 8)?
lozanna [386]
---------------------------

6 0
3 years ago
N to the second power - 5 in - 1 in equals 6​
Wittaler [7]

Answer:

the question is incorrect.

4 0
3 years ago
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