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castortr0y [4]
3 years ago
10

Which expression is equivalent to (a^-3 b/a^-5 b3)^-3? Assume a=0, b=0.

Mathematics
1 answer:
prohojiy [21]3 years ago
7 0
Use:\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\(a^n)^m=a^{nm}\\\\a^{-n}=\dfrac{1}{a^n}\\\\(ab)^n=a^nb^n

\left(\dfrac{a^{-3}b}{a^{-5}b^3}\right)^{-3}=\left(a^{-3-(-5)}b^{1-3}\right)^{-3}=\left(a^{-3+5}b^{-2}\right)^{-3}=\left(a^2b^{-2}\right)^{-3}\\\\=(a^2)^{-3}(b^{-2})^{-3}=a^{2(-3)}b^{-2(-3)}=a^{-6}b^6=\dfrac{b^6}{a^6}
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Use the numbers 1-12 one time each to creat four true statements with addition, multiplication, subtraction and division
laila [671]

If you mean that you can only use each number along the four expressions, it looks impossible to me. Here's the proof.

Multiplications and divisions are the most restrictive operations, because only some triplets will work. In particular, you can choose

(2,3,6),\ (2,4,8),\ (2,5,10),\ (2,6,12),\ (3,4,12)

I'm listing them in triplets because you can use them in many ways. For example, the first triple can be used to generate

2\cdot 3 = 6,\quad 3\cdot 2 = 6,\quad 6\div 3 = 2,\quad 6\div 2 = 3

But it doesn't really matter, in all cases you used numbers 2,3, and 6.

If you look closely, all triplets but the last one involve 2. This means that we must use the last one, because otherwise we would use two triplets with two, and we would have repetitions.

So, we surely have to use (3,4,12), either to write 3\cdot 4=12 or 12\div 4=3.

This means that we can't use 3, 4 and 12 anymore. The only triplet remaining is (2,5,10).

For example, let's say that our multiplication is 2\cdot 5 = 10 and our division is 12\div 4 = 3.

We're left with the following numbers:

1,\ 6,\ 7,\ 8,\ 9,\ 11

From here, we're left with a few choices for the addition: if we choose 1+6=7 we're left with 8,9 and 11. We can't write any subtraction with these numbers.

If we choose 1+7=8, we're left with 6, 9 and 11. We can't write any subtraction with these numbers.

If we choose 1+8=9, we're left with 6, 7 and 11. We can't write any subtraction with these numbers.

To recap, we're forced to use 2,3,4,5,10 and 12 for the multiplication and the division, and the remaining numbers don't allow to write an addiction and a subtraction.

Thus, you can't use all the operations involving numbers 1-12 only once.

7 0
3 years ago
Question 3
tino4ka555 [31]
Hey guys I’m so sorry I don’t really have an answer
5 0
2 years ago
What basic multiplication fact can help you divide 18÷3?
Temka [501]
D is the answer

18/3= 6

and 6*3= 18

I hope this helps!
6 0
3 years ago
Read 2 more answers
What is StartFraction 11 Over 12 EndFraction divided by one-third? A fraction bar labeled 1. Under the 1 are 3 boxes labeled one
Sav [38]

Answer:

<h2>2 and three-fourths </h2>

Step-by-step explanation:

Given the expression \frac{11}{12}/\frac{1}{3}, the equivalent expression can be gotten as shown;

= \frac{11}{12}/\frac{1}{3}\\= \frac{11}{12}*\frac{3}{1}\\  = \frac{11}{4} \\= 2+\frac{3}{4}\\ = 2\frac{3}{4}

2 and three-fourth therefore gives the required expression

8 0
3 years ago
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I need help quick!!<br><br> you can have brainliest this is algerbra btw
padilas [110]

Answer:

Step-by-step explanation:

Day 1 = 2 birds

day 2 = 3 birds

day 3 = 9 birds

day 4 = 8 birds

day 5 = 1 bird

On day 1 the points are (1,2)

On day 5 the points are (5,1)

(I am picking these for the points because I don't know your options for the selecting area.)

we use this formula y2-y1/x2-x1

2-5/1-1

3/0

our answer is infinite which is the relation and this is an infinite function

5 0
2 years ago
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