The value of  5^{151} in  U_{7} is?

Q: formula for the n^th triangular number is n(n+1)/2. Prove it.

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Q: n be a positive natural nun (an)" is equivalent to: 4n Let a) n²n (n²-4n) b) n(n²^_^) d) na^ (^^-2^)…

A: Given, n4n-(2n)2n

Q: Use notation by explicitly listing all the members of each rhs {???} to complete the following…

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Q: Find the order of 5 modulo 2^100.

A:

Q: Evaluate (6 – 5)^2 by working within the parentheses first. Evaluate 6^2 – 5^2. Compare the answer…

A: Evaluate (6 – 5)^2 Evaluate 6^2 – 5^2.

Q: what is aba^-1 in algebra and what is it used for?

A: In algebra, the expression "" represents the product of a group element "a" with its inverse "a^-1".…

Q: Q2. If (16*) (256) = 46, then find 40(9*+9-x) 9x-9-x

A: The given expression is 16x(256)=46 We have to find the 409x+9-x9x-9-x

Q: 14 nC AU Conc=

A: Defination: n(A∪B)=n(A)+n(B)-n(A∩B) n(A∩B): common area of A and B n(A∩B∩C):Common area of A,B and C

Q: how many different bases can R^2 and R^3 have?

A: Explain about the count of number of bases of ℝ2 and ℝ3.

Q: What is the coefficient of the term x^3y^2 expansion of (3x - y2)4?

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Q: 1.) Predict the next term 2, 0, -18, -64, -150, -288,- 490

A: Note: according to our guidelines we can answer only first question

Q: 4s-5 Find L 8s+9 s2-8s+9

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Q: Which member of binomial expansion of (2x^3 + x^-1)^10 contains x^6 ?

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Q: Abstract Algebra: show that (a*b)^-1 = a^-1 * b^-1 implies a*b=b*a

A: Properties of group G aa-1=e(ab)-1=b-1a-1ae=ea=a

Q: P=2^(43112609)-1 Suppose you have traveled to a faraway place where the base of the number system is…

A:

Q: 10) Simplify the expression, writing your final answer with a positive exponent 5t^-2-2t^-5 O 10t*10…

A: Given expression is: 5t^-2.2t^-5

Q: شي/ عبمناسر العالتنةد درشا د dy يدتدا

A: We have to find integration for the given function.       NOTE - According to our guidelines we can…

Q: By considering uniqueness of factorization of integers, find all pairs (x, y) ∈ N^2 such that x^2 −…

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Q: Please solve.  a) 6^x+3=1/216 b) 8^X+2=(1/4)^x+3 c) 5(3)^x=135

A: a) 6x+3=12166x+3=1636x+3=6-3x+3=-3  [Equate the exponents]x=-6

Q: The r’s complement of an n-digit number N in base r is defined as r^n - N for N ≠ 0 and 0 for N = 0.…

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Q: Compute phi(6^2 x 4^3). (Note that this is not a prime power factorization.)

A:

Q: Compute sigma(2^3 x 5^2 x 4^2).

A: Given: We have to compute

Q: Use the Euler Theorem to calculate 17^81(mod 55)

A:

Q: in the expansion of (x^2-(1/2x))^5 ) what is the coefficient of x^4?

A: Given that  (x2-12x)5 Apply binomial theorem:a+bn=∑i=0nnian-ibiHere,a=x2,  b=-12x ∑i=055ix25-i-12xi

Q: Find the 7-adic expansion of 1/2 up through the 7^3 power

A: jyujhjyukjhjkkhjjghfgf

Q: Using Euler’s Theorem, find the last two digits of 4444^3333

A: Let us find the last two digit of the given expression by using Euler's Theorem in the next steps.

Q: How many even 11-digit numbers (no leading zeros) have at least three 3’s?  Is it possible to use…

A: Let U be the universal set of all even 11- digit numbers( no leadingzeros)Let A be the set of all…

Q: the product of powe (3*2^(15))(2^(12))

A: