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IgorC [24]
3 years ago
15

Simplify the expression and rewrite in rational exponent form.

Mathematics
1 answer:
Dahasolnce [82]3 years ago
5 0

Answer:

4 x^{\frac{11}{10}} \cdot y^{\frac{17}{3}}

Step-by-step explanation:

The given expression: 4 \sqrt[5]{x^{3}} \cdot y^{4} \cdot \sqrt{x} \cdot \sqrt[3]{y^{5}}

Step 1: Change radical to fractional exponent.

Formula for fractional exponent: \sqrt[n]{a}=a^{\frac{1}{n}}

The power to which the base is raised becomes the numerator and the root becomes the denominator.

\Rightarrow 4 x^{\frac{3}{5}} \cdot y^{4} \cdot x^{\frac{1}{2}} \cdot y^{\frac{5}{3}}  

Step 2: Apply law of exponent for a product a^{m} \times a^{n}=a^{m+n}  

Multiply powers with same base.

\Rightarrow 4 x^{\frac{3}{5}+\frac{1}{2}} \cdot y^{4+\frac{5}{8}}  

Take LCM for the fractions in the power.

\Rightarrow 4 x^{\frac{6}{10}+\frac{5}{10}} \cdot y^{\frac{12}{3}+\frac{5}{3}}  

\Rightarrow 4 x^{\frac{11}{10}} \cdot y^{\frac{17}{3}}

Hence the simplified form of 4 \sqrt[5]{x^{3}} \cdot y^{4} \cdot \sqrt{x} \cdot \sqrt[3]{y^{5}} \text { is } 4 x^{\frac{11}{10}} \cdot y^{\frac{17}{3}}.

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polet [3.4K]

Answer:

(1/2,-5/2)

Step-by-step explanation:

\frac{ - 3 + 4 }{2}  = \frac{1}{2}  \\   \frac{ - 4 +  - 1}{2}  =   \frac{ - 5}{2}

7 0
2 years ago
Read 2 more answers
I NEED THIS ASAP, PLEASE HELP!!!
WINSTONCH [101]

Answer: 22.5 ; 5 ; 14

Step-by-step explanation:

Given the dataset:

{20,22,23,24,26,26,28,29,30}

The lower quartile (Q1) = 1/4(n + 1)th term

Where n = number of observations, n = 9

Q1 = 1/4 (9 + 1)th term

Q1 = 1/4(10) = 2.5

We average the 2nd and 3rd term:

(22 + 23) / 2

45 / 2 = 22.5

B) The interquartile range(IQR) of the dataset :

{62,63,64,65,67,68,68,68,69,74}

IQR = Q3 - Q1

The lower quartile (Q1) = 1/4(n + 1)th term

Where n = number of observations, n = 10

Q1 = 1/4 (10 + 1)th term

Q1 = 1/4(11) = 2.75 term

We take the average of the 2nd and 3rd term:

(63 + 64) / 2

45 / 2 = 63.5

The upper quartile (Q3) = 3/4(n + 1)th term

Where n = number of observations, n = 10

Q3 = 3/4 (10 + 1)th term

Q3 = 3/4(11) = 8.25 term

We take the average of the 8th and 9th term:

(68 + 69) / 2

137 / 2 = 68.5

IQR = Q3 - Q1

IQR = 68.5 - 63.5

IQR = 5

C) give the dataset :

{7,8,8,9,10,12,13,15,16}

The upper quartile (Q3) = 3/4(n + 1)th term

Where n = number of observations, n = 9

Q3 = 3/4 (9 + 1)th term

Q3 = 3/4(10) = 7.5 term

We take the average of the 7th and 8th term:

(13 + 15) / 2

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7 0
3 years ago
Which of the following fractions is greater than -4/5 but less than -3/4
choli [55]

Answer:

B. -19/25

Step-by-step explanation:

You are looking for an answer that is greater than -4/5 (which is equal to -0.80) but less than -3/4 (which is equal to -0.75). So, you can easily convert the fractions to decimals by dividing.

-33/50 = -0.66, which is greater than -0.75, so it can be eliminated.

-19/25 = -0.76, which fits our parameters, so it is the answer.

-19/20 = -0.95, which is less than -0.80, so it can be eliminated.

-7/10 = -0.70, which is greater than -0.75, so it can be eliminated.

7 0
3 years ago
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bixtya [17]

Answer:111

the purse was 1/4 so. we have to do

37.00x4 we get 148 then. we do 148-37 to get a total of 111 (:

Step-by-step explanation:

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2 years ago
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MariettaO [177]
Since p is the midpoint then xp and pay must equal each other
So, 11-6b=6-b
Solve for b
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-6 -6
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5=5b
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xp=11-6(1)
xp=5
5 0
3 years ago
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