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  • Question
  • (4 x 4 x 4 x 4 x 4 x 4) 5 x (4 x 4 x 4 ) 8 ÷ (4) 3 = (64) ?


  • Options
  • A. 17
  • B. 10
  • C. 16
  • D. 11

  • Correct Answer
  • 17 

    Explanation

    (4 x 4 x 4 x 4 x 4 x 4)5 x (4 x 4 x 4)8 ÷ (4)3 = (64)?
    Apply the law of Fractional Exponents and Laws of Exponents
    if a multiply n times a x a x a x....up to n times, then
    a x a x a x a ......up to n times = an
    By simplifying the equation
    ? (46)5 x (43)8 x 1/(4)3 = (43)?
    ? (4)30 x (4)24/(4)3 = (4)3 x ?
    ? 430 + 24 - 3 = 43 x 7
    And comparing the exponents both the sides
    ? 451 = 43 x ? ? 3 x ? = 51
    ? ? = 51/3 = 17


  • Simplification problems


    Search Results


    • 1. 
      If a * b = a + b + a / b, Then the value of 12 * 4 is

    • Options
    • A. 48
    • B. 19
    • C. 20
    • D. 21
    • Discuss
    • 2. 
      If a 2 + b 2 = a, then the value of a 12 + a 6 + 1 is?

    • Options
    • A. 2
    • B. 3
    • C. -3
    • D. 1
    • Discuss
    • 3. 
      (2.247) 3 + (1.730) 3 + (1.023) 3 -3 x 2.247 x 1.730 x 1.023 / [(2.247) 2 + (1.730) 2 + (1.023) 2 - 2.247 x 1.730 - 1.730 x 1.023 - 2.247 x 1.023] =?

    • Options
    • A. 1.730
    • B. 4
    • C. 5
    • D. 5.247
    • Discuss
    • 4. 
      5 - [3/4 +{2 1/ 2 - (1/2 + 1/6 - 1/7 )}]/2 =?

    • Options
    • A. 123/168
    • B. 223/168
    • C. 323/168
    • D. 423/168
    • Discuss
    • 5. 
      City A has a population of 136000 which is decreasing at the rate of 2400 per year , City B has a population of 84000 which is increasing at the rate of 1600 per year . In how many years will the population of two cities become equal ?

    • Options
    • A. 15
    • B. 18
    • C. 13
    • D. 19
    • Discuss
    • 6. 
      3x + 2y = 12 and xy = 6, them the value of 9x2 + 4y2 is?

    • Options
    • A. 76
    • B. 80
    • C. 72
    • D. 74
    • Discuss
    • 7. 
      If x + 1/x = 3, then x5 + 1/x5 is equal to?

    • Options
    • A. 123
    • B. 83
    • C. 92
    • D. 112
    • Discuss
    • 8. 
      If x + 1/x = 2, then what is value of x - 1/x ?

    • Options
    • A. 0
    • B. 1
    • C. 2
    • D. -2
    • Discuss
    • 9. 
      If x + 1/x = 6, then x 4 + 1/x 4 is?

    • Options
    • A. 1152
    • B. 1154
    • C. 1148
    • D. 1150
    • Discuss
    • 10. 
      If x + y = 18 and xy = 72, what is the value of x2 + y2?

    • Options
    • A. 120
    • B. 90
    • C. 180
    • D. Cannot be determined
    • Discuss


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