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Arisa [49]
3 years ago
11

Use the rules of exponents to simplify the expressions. Match the expression with its equivalent value.

Mathematics
1 answer:
Lelechka [254]3 years ago
3 0

Answer:

1) \frac{(-2)^{-5}}{(-2)^{-10}}=-32

2) 2^{-1}.2^{-4} = \frac{1}{32}

3) (-\frac{1}{2} )^3.(-\frac{1}{2} )^2=-\frac{1}{32}

4) \frac{2}{2^{-4}} = 32

Step-by-step explanation:

1) \frac{(-2)^{-5}}{(-2)^{-10}}

Solving using exponent rule: a^{-m}=\frac{1}{a^m}

\frac{(-2)^{-5}}{(-2)^{-10}}\\=(-2)^{-5+10}\\=(-2)^{5}\\=-32

So, \frac{(-2)^{-5}}{(-2)^{-10}}=-32

2) 2^{-1}.2^{-4}

Using the exponent rule: a^m.a^n=a^{m+n}

We have:

2^{-1}.2^{-4}\\=2^{-1-4}\\=2^{-5}

We also know that: a^{-m}=\frac{1}{a^m}

Using this rule:

2^{-5}\\=\frac{1}{2^5}\\=\frac{1}{32}

So, 2^{-1}.2^{-4} = \frac{1}{32}

3) (-\frac{1}{2} )^3.(-\frac{1}{2} )^2

Solving:

(-\frac{1}{2} )^3.(-\frac{1}{2} )^2\\=(-\frac{1}{8} ).(\frac{1}{4} )\\=-\frac{1}{32}

So, (-\frac{1}{2} )^3.(-\frac{1}{2} )^2=-\frac{1}{32}

4) \frac{2}{2^{-4}}

We know that: a^{-m}=\frac{1}{a^m}

\frac{2}{2^{-4}}\\=2\times 2^4\\=2(16)\\=32

So, \frac{2}{2^{-4}} = 32

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The function c=1.50(n-2)+5.50
qwelly [4]

Answer:

c =1.50n +2.50

Step-by-step explanation:

c=1.50(n-2)+5.50

The first step is to distribute the 1.5

c= 1.50*n -1.50*2 + 5.50

c = 1.50n - 3.0 +5.50

Now we need to combine like terms

c =1.50n +2.50


3 0
3 years ago
Ms. drake invests $1000 at a simple interest rate of 8.5% for 2 years. how much interest will she earn in this time?
PilotLPTM [1.2K]

Ms. Drake will earn \$ 170 in this time from the investment of \$ 1000 at a simple interest with rate of interest 8.5\%

<h3>What is the definition of simple interest?</h3>

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Conversely, for compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

Formula for finding simple interest is \frac{principal \times rate \ of \ interest \times time}{100}

Given principal of Ms. Drake is \$1000

Rate of interest is 8.5 \%

Time is 2 years.

Interest =\frac{1000 \times 8.5 \times 2}{100}

            =\frac{17000}{100}\\=170

Therefore, Ms. Drake will earn \$ 170 in this time.

To learn more about simple interest from the given link

brainly.com/question/7639734

#SPJ4

7 0
1 year ago
At pizza express it takes 6 cups of cheese to make 15 pizzas. At perfect pizza it takes 4 cups of cheese to make 6 pizzas. If th
rodikova [14]

Pizza Express has a larger constant of proportionality than Perfect Pizzas because <u><em>1.6 > 1.5</em></u>

15/6        6/4

<em>   Simplify</em>

<u>5/3    >    3/2</u>

<em>PE: 5/3 or 1.6</em>

<em>PP: 3/2 or 1.5</em>

<em />

I had this on my math test

4 0
3 years ago
The General Social Survey asked a large number of people how much time they spent watching TV each day. The mean number of hours
DerKrebs [107]

Answer:

Yes, we can conclude that the population standard deviation of TV watching times for teenagers is less than 2.66

Step-by-step explanation:

H0 : σ² = 2.66²

H1 : σ² < 2.66²

X²c = (n - 1)*s² ÷ σ²

sample size, n = 40

Sample standard deviation, s = 1.9

X²c = ((40 - 1) * 1.9²) ÷ 2.66²

X²c = 140.79 ÷ 7.0756

X²c = 19.897

Using a confidence level of 95%

Degree of freedom, df = n - 1 ; df = 40 - 1 = 39

The critical value using the chi distribution table is 25.6954

Comparing the test statistic with the critical value :

19.897 < 25.6954

Test statistic < Critical value ; Reject the Null

Hence, we can conclude that the population standard deviation of TV watching times for teenagers is less than 2.66

8 0
3 years ago
What is the value of 4 in 0.543
BabaBlast [244]
The value of 4 is 4 hundredths.
5 0
3 years ago
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