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3 years ago

9

Choose the correct simplification of the expression the quantity a to the 2nd power over b to the 3rd power all raised to the 4t

h power.

1 answer:

kifflom [539]3 years ago

7 0

The answer will be a^8 over b^12.

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0/1 For positive integer n, n? = n! · (n − 1)! · … · 1! And n# = n? · (n − 1)? · … · 1?. What is the value of 4# · 3# · 2# · 1#?

MakcuM [25]

Answer:

331776

Step-by-step explanation:

Since n? = n! · (n − 1)! · … · 1! And n# = n? · (n − 1)? · … · 1?

Then 4# = 4? · (4 − 1)? · (4 − 2)?· 1?

= 4? · 3? · 2?· 1?

Now, n? = n! · (n − 1)! · … · 1!

So, 4? = 4! · (4 − 1)! · (4 − 2)! · 1! = 4! · 3! · 2! · 1! = 288

Thus, 3? = 3! · (3 − 1)! · 1! = 3! · 2! · 1! = 12

Also, 2? = 2! · (2 − 1)! · 1! = 2! · 1! · 1! = 2

and 1? = 1! · (1 − 1)! · 1! = 1! · 0! · 1! = 1

So, 4# = 4? · 3? · 2?· 1? = 288 × 12 × 2 × 1 = 6912

We now find 3#

3# = 3? · (3 − 1)? · 1? = 3? · 2?· 1?

Now, n? = n! · (n − 1)! · … · 1!

So, 3? = 3! · (3 − 1)! · 1! = 3! · 2! · 1! = 12

Thus, 2? = 2! · (2 − 1)! · 1! = 2! · 1! · 1! = 2

and, 1? = 1! · (1 − 1)! · 1! = 1! · 0! · 1! = 1

So, 3# = 3? · 2?· 1? = 12 × 2 × 1 = 24

We now find 2#

2# = 2? · (2 − 1)? · 1? = 2? · 1?· 1?

Now, n? = n! · (n − 1)! · … · 1!

So, 2? = 2! · (2 − 1)! · 1! = 2! · 1! · 1! = 2

1? = 1! · (1 − 1)! · 1! = 1! · 0! · 1! = 1

So, 2# = 2?· 1? = 2 × 1 = 2

We now find 1#

1# = 1? · 1? = 1? · 1?

Now, n? = n! · (n − 1)! · … · 1!

So, 1? = 1! · (1 − 1)! · 1! = 1! · 0! · 1! = 1

And, 1# = 1? · 1? = 1 × 1 = 1

So, 4# · 3# · 2# · 1#? = 6912 · 24 · 2 · 1? = 331776

7 0

3 years ago

Help please need this answer

Arte-miy333 [17]

Answer:

this questoin has many soulutoins so c

Step-by-step explanation:

4 0

3 years ago

Katena32 [7]

Answer: 60cm

Step-by-step explanation:

6 times 2 is 12

12 times 5 is 60

5 0

3 years ago

It takes 1 1/2 hours to fill 1/2 of a tank how long will it take to fill 2 tanks completely

Likurg_2 [28]

Answer:

15

Step-by-step explanation:

hope this helps

4 0

2 years ago

The sum of three integers is 92. The second number is three times the first number. The third number is ten less than twice the

SVEN [57.7K]

Given,
The sum of three integers is 92

So,
Let,
The first integer be "x"
The second integer be "y"
The third integer be "z"

Now,
According to the question,
y = 3x ..............equation (1)
z = 2x - 10 .............. equation (2)
x + y + z = 92 ..............equation (3)

Now,
Substituting the value of "y" and "z" from equation (1) and (2), we get,

x + (3x) + (2x - 10) = 92
x + 3x + 2x - 10 = 92
6x - 10 = 92
6x = 92 + 10
x = 102 / 6
x = 17

Now,
substituting the value of "x" in equation (1)
y = 3 (17)
y = 51

Now,
Substituting the value of "x" in equation (2),

z = 2 (17 ) - 10
z = 34 - 10
z = 24

So, the numbers are 17, 51 and 24

NEVER HATE MATH!!!

3 0

3 years ago