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exponent

  1. math_celebrity

    If 2^x + 2^x + 2^x + 2^x = 2^16, what is the value of x?

    If 2^x + 2^x + 2^x + 2^x = 2^16, what is the value of x? Add up the left side, we get: 4(2^x) = 2^16 But 4 = 2^2, so we have: 2^2(2^x) = 2^16 Using our exponent rule, we have: 2^(x + 2) = 2^16 x + 2 = 16 Subtract 2 from each side, we get: x = 14
  2. math_celebrity

    Simplify 3^n + 3^n + 3^n

    Since we have all coefficients of 3 raised to the n, we have: 3(3^n) Using our exponent rules, we have: 3^(n + 1)
  3. math_celebrity

    3 = b^y. Then 3b = ?

    a. b^(y + 1) b. b^(y + 2) c. b^(y + 3) d. b^2y e. b^3y Multiply each side by b: 3b = b^y * b 3b = b^(y + 1) answer A.
  4. math_celebrity

    (2x10^3) x (2x10^6) x (2x10^12) = ?

    Multiply the 2's together: 2 x 2 x 2 = 8 Multiply the 10 with exponent terms together: 10^3 x 10^6 * 10^12 = 10^(3 + 6 + 12) = 10^21 Group both results: 8 x 10^21
  5. math_celebrity

    Find the last digit of 7^2013

    Consider the first 8 calculations of 7 to an exponent: 7^1 = 7 7^2 = 49 7^3 = 343 7^4 = 2,401 7^5 = 16,807 7^6 = 117,649 7^7 = 823,543 7^8 = 5,764,801 Take a look at the last digit of the first 8 calculations: 7, 9, 3, 1, 7, 9, 3, 1 The 7, 9, 3, 1 repeats through infinity. So every factor of...
  6. math_celebrity

    Find the last digit of 2 raised to the 2020 no calculator

    Check out this pattern: 2^1= 2 2^2= 4 2^3 = 8 2^4= 16 2^5 = 32 2^6 = 64 2^7 = 128 2^8 = 256 The last digit repeats itself in blocks of 4 2, 4, 8, 6 We want to know what is the largest number in 1, 2, 3, 4 that divides 2020 without a remainder. LEt's start with 4 and work backwards. 2020/4 =...
  7. math_celebrity

    Simplify 6x^2y^3(2x^2y)^3

    Simplify the monomial in parentheses: 2^3x^2*3y^3 8x^6y^3 Now we update the multiplication: 6x^2y^3(8x^6y^3) 6*8 x^(2 + 6)y^(3 + 3) 48x^8y^6
  8. math_celebrity

    Simplify 2^4 x 8^7

    We know that 2^3 = 8, so we can rewrite this as: 2^4 x (2^3)^7 (2^3)^7 = 2^3 * 7 = 2^21 2^4 x 2^21 2^(4 + 21) 2^25
  9. math_celebrity

    Given that m is a positive integer and 4^m - 1 = n, which of the following values CANNOT represent n

    A. 3 B. 7 C. 63 D. 255 We know that: 4^1 = 4 4^2 = 16 4^3 = 64 4^4 = 256 4^5 = 1024 4^6 = 4096 Notice they all end in 4 or 6. This continues for to infinity. 4^m will either end in a 4 or a 6 Therefore, 4^m - 1 ends in: 4 - 1 = 3 6 - 1 = 5 Choices A, C, and D end in 3 or 5. Choice B...
  10. math_celebrity

    Find the last digit of 4^2081 no calculator

    Find the last digit of 4^2081 no calculator 4^1= 4 4^2 = 16 4^3 = 64 4^4 = 256 4^5 = 1024 4^6 = 4096 Notice this pattern alternates between odd exponent powers with the result ending in 4 and even exponent powers with the result ending in 6. Since 2081 is odd, the answer is 4.
  11. math_celebrity

    3^14/27^4 = ?

    3^14/27^4 = ? Understand that 27 = 3^3. Rewriting this, we have: 3^14/(3^3)^4 Exponent identity states (a^b)^c = a^bc, so we have: 3^14/3^12 Simplifying, we have: 3^(14 - 12) = 3^2 = 9
  12. math_celebrity

    3 power to what gets me 81

    3 power to what gets me 81 Let x be our power: 3^x = 81 3 * 3 * 3 * 3 = 81 So x = 4: 3^4 = 81
  13. math_celebrity

    A new company is projecting its profits over a number of weeks. They predict that their profits each

    A new company is projecting its profits over a number of weeks. They predict that their profits each week can be modeled by a geometric sequence. Three weeks after they started, the company's projected profit is $10,985.00 Four weeks after they started, the company's projected profit is...
  14. math_celebrity

    Bill and nine of his friends each have a lot of money in the bank. Bill has 10^10 dollars in his acc

    Bill and nine of his friends each have a lot of money in the bank. Bill has 10^10 dollars in his acc All nine of Bill's friends pooled together is: 9 * 10^9 Bill's 10^10 can be written as 10 * 10^9 So Bill's is greater
  15. math_celebrity

    Some scientists believe that there are 10^87 atoms in the entire universe. The number googolplex is

    Some scientists believe that there are 10^87 atoms in the entire universe. The number googolplex is a 1 followed by a googol of zeros. If each atom in the universe is used as a zero, how many universes would you need in order to have enough zeros to write out completely the number googolplex...
  16. math_celebrity

    If there are 10^30 grains of sand on Beach A, how many grains of sand are there on a beach the has 1

    If there are 10^30 grains of sand on Beach A, how many grains of sand are there on a beach the has 10 times the sand as Beach A? (Express your answer using exponents.) 10^30 * 10 = 10^(30 + 1) = 10^31
  17. math_celebrity

    1^10 = ?

    1^10 = ? 1^10 = 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 1^10 = 1
  18. math_celebrity

    9, 3, 1, 1/3, 1/9 What is the next number in this sequence? What is the function machine for this se

    9, 3, 1, 1/3, 1/9 What is the next number in this sequence? What is the function machine for this sequence? We see the following pattern in this sequence: 9 = 9/3^0 3 = 9/3^1 1 = 9/3^2 1/3 = 9/3^3 1/9 = 9/3^4 Our function machine formula is: f(n) = 9/3^(n - 1) Next term is the 6th term: f(6)...
  19. math_celebrity

    3, 6, 12, 24, 48 What is the function machine for this sequence?

    3, 6, 12, 24, 48 What is the function machine for this sequence? We see the following pattern: 3 * 2^0 = 3 3 * 2^1 = 6 3 * 2^2 = 12 3 * 2^3 = 24 3 * 2^4 = 48 Our function machine for term n is: f(n) = 3 * 2^(n - 1)
  20. math_celebrity

    1, 1/2, 1/4, 1/8, 1/16 The next number in the sequence is 1/32. What is the function machine you wou

    1, 1/2, 1/4, 1/8, 1/16 The next number in the sequence is 1/32. What is the function machine you would use to find the nth term of this sequence? Hint: look at the denominators We notice that 1/2^0 = 1/1 = 1 1/2^1 = 1/2 1/2^2 = 1/4 1/2^3 = 1/8 1/2^4 = 1/32 So we write our explicit formula for...
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