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hammer [34]
3 years ago
7

Simplify the expression.​ (Do not evaluate the exponents on coefficients in the​ answer.)

Mathematics
1 answer:
ycow [4]3 years ago
8 0

Answer:

(-6)^5p^5

Step-by-step explanation:

To evaluate or simplify expressions with exponents, we use exponent rules.  

1. An exponent is only a short cut for multiplication. It simplifies how we write the expression.

2. When we multiply terms with the same bases, we add exponents.

3. When we divide terms with the same bases, we subtract exponents.

4. When we have a base to the exponent of 0, it is 1.

5. A negative exponent creates a fraction.

6. When we raise an exponent to an exponent, we multiply exponents.

7. When we have exponents with parenthesis, we apply it to everything in the parenthesis.

We will use these rules 2 and 7 to simplify.  First apply the 4 exponent to both -6 and p. Then add the exponent of the base -6 and p on the outside of the parenthesis.

(-6p)^4(-6p)\\(-6)^4p^4*-6*p\\(-6)^5p^5

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So twin primes are prime numbers that have a difference of 2. The ones between 25 and 55 are (29,31) and(41,43). Hope that helps
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Simplify (5 + 1)2 - (11 + 32) + 4.
4vir4ik [10]

Answer:

6

Step-by-step explanation:

The trick here is to know PEMDAS.

PEMDAS stands for: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

This is the order in which you should simplify a problem.

Parentheses:

   (5 + 1)^2 - (11 + 32) + 4

   (6)^2 - (43) + 4

Exponents:

   (6)^2 - (43) + 4

   36 - 34 + 4

We have no multiplication or division, so we can skip those steps.

Addition:

   36 - 34 + 4

   40 - 34

Subtraction:

   40 - 34

   6

So 6 is our answer.

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The average annual salary of the employees of a company in the year 2005 was $80,000. It increased by the same factor each year
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Directed line segment has endpoints P(– 8, – 4) and Q(4, 12). Determine the point that partitions the directed line segment in a
larisa86 [58]

Answer:

Point (1,8)  

Step-by-step explanation:

We will use segment formula to find the coordinates of point that will partition our line segment PQ in a ratio 3:1.

When a point divides any segment internally in the ratio m:n, the formula is:

[x=\frac{mx_2+nx_1}{m+n},y= \frac{my_2+ny_1}{m+n}]

Let us substitute coordinates of point P and Q as:

x_1=-8,

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x_2=4

y_2=12

m=3

n=1

[x=\frac{(3*4)+(1*-8)}{3+1},y=\frac{(3*12)+(1*-4)}{3+1}]

[x=\frac{12-8}{4},y=\frac{36-4}{4}]

[x=\frac{4}{4},y=\frac{32}{4}]

[x=1,y=8]

Therefore, point (1,8) will partition the directed line segment PQ in a ratio 3:1.

   

7 0
3 years ago
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