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  1. math_celebrity

    10, 1,000, 100,000, 10,000,000 What power of 10 is the 80th term?

    10, 1,000, 100,000, 10,000,000 What power of 10 is the 80th term? We see the following pattern 10^1 = 10 10^3 = 1000 10^5 = 100,000 10^7 = 10,000,000 f(n) = 10^(2n - 1) We build the 80th term: f(80) = 10^(2(80) - 1) f(80) = 10^(160 - 1) f(80) = 10^159
  2. math_celebrity

    1, 8, 27, 64 What is the 10th term?

    1, 8, 27, 64 What is the 10th term? We see the following pattern: 1^3 = 1 2^3 = 8 3^3 = 27 4^3 = 64 We build our sequence function using this pattern: f(n) = n^3 With n = 10, we have: f(10) = 10^3 f(10) = 1,000
  3. math_celebrity

    2^n = 4^(n - 3)

    2^n = 4^(n - 3) 2^n = (2^2)^(n - 3) (2^2)^(n - 3) = 2^2(n - 3) 2^n= 2^2(n - 3) Comparing exponents, we see that: n = 2(n - 3) n = 2n - 6 Subtract n from each side: n - n = 2n - n - 6 0 = n - 6 n = 6
  4. math_celebrity

    5^(n - 1) = 15,625

    5^(n - 1) = 15,625 We know 5^6 = 15,625, so we have: n - 1 = 6 Add 1 to each side: n - 1 + 1 = 6 + 1 Cancel the 1's on the left side: n = 7
  5. math_celebrity

    if x^2=y^3, for what value of z does x^{3z}= y^9

    if x^2=y^3, for what value of z does x^{3z}= y^9 y^9 = y^3 * y^3, so if we square the right side, we must square the left side for equivalence: x^2 * x^2 = x^4 Therefore, x^4 = y^9 Going back to our problem, x^{3z}= y^9, so 3z = 4 Divide each side by 3 to isolate z, and we have: 3z/3 = 4/3...
  6. math_celebrity

    raise b to the 6th power then find the sum of the result and 4

    raise b to the 6th power then find the sum of the result and 4 raise b to the 6th power b^6 raise b to the 6th power then find the sum of the result and 4 b^6 + 4
  7. math_celebrity

    3x to the power 2n

    3x to the power 2n We take the expression 3x raise it to the power of 2n (3x)^2n
  8. math_celebrity

    The square of the difference of n and 2, increased by twice n

    The square of the difference of n and 2, increased by twice n The difference of n and 2: n - 2 The square of the difference of n and 2 means we raise (n - 2) to the 2nd power: (n - 2)^2 Twice n means we multiply n by 2: 2n The square of the difference of n and 2, increased by twice n (n -...
  9. math_celebrity

    c varies jointly as the square of q and cube of p

    c varies jointly as the square of q and cube of p The square of q means we raise q to the 2nd power: q^2 The cube of p means we raise p to the rdd power: p^3 The phrase varies jointly means there exists a constant k such that: c = kp^3q^2
  10. math_celebrity

    The cube of x is less than 15

    The cube of x is less than 15 The cube of x means we raise x to the 3rd power: x^3 Less than 15 means we setup the following inequality x^3 < 15
  11. math_celebrity

    How many times bigger is 3^9 than 3^3

    How many times bigger is 3^9 than 3^3 Using exponent rules, we see that: 3^9 = 3^3 * 3^6 So our answer is 3^6 times bigger
  12. math_celebrity

    the square of the sum of 2a and 3b

    the square of the sum of 2a and 3b the sum of 2a and 3b 2a + 3b The square of this sum means we raise 2a + 3b to the 2nd power: (2a + 3b)^2
  13. math_celebrity

    -x squared

    -x squared We take -x and raise it to the 2nd power: (-x)^2 = -x * -x = x^2
  14. math_celebrity

    the square of the sum of x and y is less than 20

    the square of the sum of x and y is less than 20 The sum of x and y means we add y to x: x + y the square of the sum of x and y means we raise the term x + y to the 2nd power: (x + y)^2 The phrase is less than means an inequality, so we write this as follows: (x + y)^2 < 20
  15. math_celebrity

    raise r to the 8th power then find the product of the result and 3

    raise r to the 8th power then find the product of the result and 3 Raise r to the 8th power means we raise r with an exponent of 8: r^8 The product of the result and 3 means we muliply r^8 by 3 3r^8
  16. math_celebrity

    r squared plus the product of 3 and s plus 5

    r squared plus the product of 3 and s plus 5 r squared means we raise r to the power of 2 r^2 The product of 3 and s means we multiply s by 3: 3s plus 5 means we add 3s + 5 R squared plus means we add r^2: r^2 + 3s + 5
  17. math_celebrity

    4(a)(a)(b)(b)(b)

    4(a)(a)(b)(b)(b) We have 2 a's and 3 b's. We write this as: 4a^2b^3
  18. math_celebrity

    cube root of a number and 7

    cube root of a number and 7 The phrase a number means an arbitrary variable, let's call it x: x Cube root of a number means we raise x to the 1/3 power: x^1/3 And 7 means we add 7: x^1/3 + 7
  19. math_celebrity

    3 less than a number times itself

    3 less than a number times itself The phrase a number means an arbitrary variable, let's call it x: x Itself means the same variable as above. So we have: x * x x^2 3 less than this means we subtract 3 from x^2: x^2 - 3
  20. math_celebrity

    ratio of the squares of t and u

    ratio of the squares of t and u Ratio is also known as quotient in algebraic expression problems. The square of t means we raise t to the power of 2: t^2 The square of u means we raise u to the power of 2: u^2 ratio of the squares of t and u means we divide t^2 by u^2: t^2/u^2
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