1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Kisachek [45]
3 years ago
14

Simplify the expression: (15-8)^9 ————— [ (5+2)^2]^3

Mathematics
1 answer:
horsena [70]3 years ago
7 0

Answer:

343

Step-by-step explanation:

Remember the order of operations you have to solve in, or PEMDAS, which stands for parentheses, exponents, multiplication and division (left to right, whichever one is leftmost do first), and addition and subtraction (left to right, the same as stated earlier).

1) First, simplify what it's inside the innermost parentheses:

\frac{(15-8)^9}{[(5+2)^2]^3} \\= \frac{(7)^9}{[(7)^2]^3} \\

= \frac{(7)^9}{[7^2]^3} \\

2) To make things easier, you don't actually have to multiply out 7 to the ninth power on the numerator yet. You can keep it there for now. Instead, just distribute the exponent of 3 that's outside the brackets to the 7 squared inside - but don't multiply everything out - only multiply the exponents, writing 7^6.

= \frac{(7)^9}{[7^2]^3} \\\frac{7^9}{7^6}

3) This way, by having the same bases of 7, it is easier to solve without multiplying out huge numbers. All you have to do now is divide exponents of the same base. You only have to subtract the exponents to do this:

\frac{7^9}{7^6} \\= 7^9^-^6\\= 7^3

4) Finally, multiply 7^3 out:

= 7^3\\= (7) (7) (7) \\= 343

Thus, the answer is 343.

You might be interested in
The average weight of an adult blue whale is 365.000 pounds. Which expression represents this weight in scientific notation? A)
Elina [12.6K]
The answer is 3.65 x 10^5
7 0
2 years ago
Write an equation of the line that passes through (4,2) and is perpendicular to the line y=−13x+1.
7nadin3 [17]

Answer:

y=x-2

Step-by-step explanation:

This slope goes through the point and is perpendicular to y=-13x+1

Hope this helped

4 0
3 years ago
NEED HELP!!! Can someone help me with 5, 7, and 8??? <br> Need this asap!!!<br> THANK YOU!!!
Serjik [45]

Answer:

5) 8/17 = .471

7) 8/17 = .471

8) 15/17 = .88

Step-by-step explanation:

hope that helps

6 0
3 years ago
Read 2 more answers
Engineers must consider the diameters of heads when designing helmets. The company researchers have determined that the populati
IrinaK [193]

Answer:

1. The minimum head breadth that will fit the clientele is of 3.95-in.

2. The maximum head breadth that will fit the clientele is of 9.25-in.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 6.6-in and a standard deviation of 1.1-in.

This means that \mu = 6.6, \sigma = 1.1

1. What is the minimum head breadth that will fit the clientele?

The 0.8th percentile, which is X when Z has a p-value of 0.008, so X when Z = -2.41.

Z = \frac{X - \mu}{\sigma}

-2.41 = \frac{X - 6.6}{1.1}

X - 6.6 = -2.41*1.1

X = 3.95

The minimum head breadth that will fit the clientele is of 3.95-in.

2. What is the maximum head breadth that will fit the clientele?

The 100 - 0.8 = 99.2nd percentile, which is X when Z has a p-value of 0.992, so X when Z = 2.41.

Z = \frac{X - \mu}{\sigma}

2.41 = \frac{X - 6.6}{1.1}

X - 6.6 = 2.41*1.1

X = 9.25

The maximum head breadth that will fit the clientele is of 9.25-in.

8 0
2 years ago
A triangle has an area of 72 and a base of 10 what is the height
Studentka2010 [4]
The height will be 14.4
5 0
3 years ago
Read 2 more answers
Other questions:
  • Enter the slope-intercept equation of the line shown below.
    13·1 answer
  • What is -4(x+6) can someone pls help
    7·2 answers
  • Guys can you please to this thank
    7·1 answer
  • keith and michelle went out to dinner. the total cost of the meal including the tip came $53.70. if the combined tip came out to
    5·1 answer
  • An angle measures 27.8° more than the measure of its complementary angle. What is the measure of each angle?
    5·2 answers
  • Can someone teach me how to do this type of thing?​
    13·2 answers
  • Why is it important to look at more than the first two numbers of a pattern to decide the rule for the pattern?
    5·1 answer
  • The base of a triangle is 7 meters longer than the height of the triangle of the area of the triangle is 22 square meters what a
    9·1 answer
  • 1/7 x X =1<br> X x 1/11=1<br> 1 divided by 1/5=
    7·1 answer
  • Please answer below :)
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!