6) Write the following in expanded form using powers of 10 (1 pt cach) a) 345 b) 7321= 7) In each case, rewrite using an exponent and then find the total (1 pt each) a) 7 x 7x7 x7 b) 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = 8) In each case use the Pythagorean Theorem to determine the missing side. Show your work. Round to one decimal. (2pts cach) 32 m b). 12 km 3.7 km

Q: 680 -59 -0 - 0] q? 600 69 - - 0-01 q? - 680 DIFFREN TIATE d Pla) = q? -reo] 2 0.0) q-680] da da 600…

A: topic - differentiation

Q: 01- find the values of x and y for the following:- c) (2 + 5i)(x + yi) = (3-5i)²

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Q: 9. Solve. a) 4+6(4 *)= 5 b) 2(5) + 2(5) = 4

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Q: i) Sin 20easoal-Sin?

A: Use the trigonometric identities,…

Q: What is the value of  i) i3i3  and ii)  i6i6

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A: To verify: 2163÷83= 21683

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A: Here we have to integrate by the trigonometric substitution.  I=∫x3x2-1dx

Q: Power Rule: a) Evaluate (3') %3D b) Expand (3)³ =- c) Use the power rule to simplify (3³)³ =

A: use law of exponents to find the value of the given expression.

Q: (? ), Now So Quotient Remainder 546 546 * 345 (= 73) 203 I.3 49 (= 7²)

A: According to the given information, it is required to convert a base 10 number to base 7 number.

Q: 122

A: Solve for tha variable

Q: = Convert the following numbers using the following: 1 hr 60 min, 1 min = 60 s, 1000 m 1 km, 1.6 km…

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Q: f ydata = 12 and ymodel = 15, what is r^2? A) 9 B) 3 C) 6 D) -3

A: Solution: Given information: y data= 12 y model = 15

Q: 8) Evaluate the following without the use of a calculator arccsc(-√2)

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Q: dx 38) (x - 6)( x - 5) 7 A) In 2 B) ! In 7 C) In 6 D) - In 2 6

A: This question is based on definite integral.

Q: 22) -2 +4i -10-6i

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Q: Multiply (3 - 2i)(4 + 3i)

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Q: e (V2) re (2) = 1 réc2) = 3 then ofa (4)- 21441

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Q: Given the complex numbers, find the roots of the ff: 1) ( -1 )^1/4 2) ( -1-i )^1/3 3) ( -i )^1/3

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Q: -) Find, if possible , AB and B 31 A= B2 43 15 302 917

A: Explanation of the solution is given below...

Q: Evatuate the function at the given value of the independent vaniable. Simplity the results x) -- x)…

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Q: 2) 73°

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Q: In(√√e.e7/5)

A: First i have written two properties of logrithmic and then use the for the given problem and easily…

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Q: Simplify i231 where i is the imaginary unit and is defined as: i = √(-1).

A: Given:

Q: a) Express in terms variables, and büc= 8 where

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Q: Calculate the following: A. (17-4i) +(13+2i) B. (18+3i) -(13-2i) C. (9+2i)(2-4i)

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Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.