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erik [133]
2 years ago
9

Which expression is equivalent to 8^-3/ 2^-3? a. 4^0 b. 4^-3 c. 1/4^-3 d. 4

Mathematics
1 answer:
Fittoniya [83]2 years ago
3 0

Answer:

  b.  4^-3

Step-by-step explanation:

The expression can be simplified to a number of different levels. Here, it looks like the answer choices want you to simplify it like this:

  \dfrac{8^{-3}}{2^{-3}}=\left(\dfrac{8}{2}\right)^{-3}=\boxed{4^{-3}}

__

In this case, the applicable rule of exponents is ...

  (a/b)^c = (a^c)/(b^c)

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Neporo4naja [7]
4k-20k^9=4k(1-5k^8)=4k\left[1^2-(k^4\sqrt5)^2\right]\\\\=4k(1-k^4\sqrt5)(1+k^4\sqrt5)=4k\left[1^2-(k^2\sqrt[4]5)^2\right](1+k^4\sqrt5)\\\\=4k(1-k^2\sqrt[4]5)(1+k^2\sqrt[4]5)(1+k^4\sqrt5)\\\\=4k\left[1^2-(k\sqrt[8]5)^2\right](1+k^2\sqrt[4]5)(1+k^4\sqrt5)\\\\=4k(1-k\sqrt[8]5)(1+k\sqrt[8]5)(1+k^2\sqrt[4]5)(1+k^4\sqrt5)

3b^2-108=3(b^2-36)=3(b^2-6^2)=3(b-6)(b+6)

Used:\ (a-b)(a+b)=a^2-b^2
7 0
3 years ago
John sells appliances for a living. He sold a
Thepotemich [5.8K]

Answer:

95$!

Step-by-step explanation:

475 x 20% = 95

8 0
2 years ago
A store is having a sale on jelly beans and trail mix. For 6 pounds of jelly beans and 2 pounds of trail mix, the total cost is
Aneli [31]

Answer:

Jelly Bean price per pound = $3.25, Trail Mix price per pound = $1.25

Step-by-step explanation:

Let jb = price per pound of jelly beans

Let tm = price per pound of trail mix

equation 1 -> 6*jb + 2*tm = 22

equation 2 -> 3*jb + 5*tm = 16

simplify equation 1

6*jb + 2tm = 22

2*tm = 22 - 6*jb

divide by 2

tm = 11 - 3*jb

plug this into equation 2

3*jb + 5*tm = 16

3*jb + 5*(11-3*jb) = 16

3*jb + 55 - 15*jb = 16

-12*jb + 55 = 16

-12*jb = 16 - 55

-12*jb = -39

jb = -39/-12

jb = 3.25

then, plug the cost per pound of jelly beans back into the simplified equation 1

tm = 11 - 3*jb

tm = 11 - 3*3.25

tm = 1.25

3 0
3 years ago
I don't really understand the question so can someone help me answer the question please?​
Ksivusya [100]

Answer:

1/ 3

Step-by-step explanation:

If each of the cards is turned over, the probability of picking up a card of one type P(E) becomes equal to:

=> P(E) = number of cards of the required type/ total number of cards

● Total number of spades( ♤ ) = 3

{the queen, one ace and the nine are all spades}

● Total number of cards = 6

Probability of drawing a spade= 3/ 6

= 1/ 2

● Total number of "7" = 1

● Total number of cards = 6

Probability of drawing a 7

= 1/ 6

Now, what's asked is the difference in the probabilities of drawing a spade and a seven.

= 1/ 2 - 1/ 6

= 3/ 6 - 1/ 6

= 2/ 6

= 1/ 3

Hence, 1/ 3 of a greater chance of drawing a spade over a 7.

5 0
3 years ago
Given an exponential function for compounding interest, A(x) = P(1.02)x, what is the rate of change?
Sedbober [7]
A(x) = P(1.02)^x
A(x) = P(1 + 0.02)^x
A(x) = P(1 + r)^x

Therefore rate of change = 0.02 = 2%
6 0
3 years ago
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