Name: Carissa

Who is asking: Student
Level: Middle

Question: how do you work this out? Investigate the relationship between a,b,c and d if 2a*2b=4c/4d?

Hi Carissa, Hi Carissa,

To find the relationship between a, b, c and d, you must first know the rules of exponents:

  1. When you multiply two numbers with the same base, you add the exponents

    eg. a2 * a3 = a2+3 = a5
  2. When you divide two numbers with the same base, you subtract the exponent of the number in the denominator from the exponent of the number in the numerator.

    eg. a5/a2 = a5-2 = a3
  3. When you raise a power to another power, you multiply the exponents

    eg. (a3)2 = a2*3 = a6
You will need to apply all three of these rules to find the relationship between a, b, c and d in your problem:

2a * 2b = 4c/4d   This is given. First apply rule 1 to left-hand side
2a+b = 4c/4d   Now apply rule 2 to right-hand side
2a+b = 4c-d   We need to have the same base on both sides, so re-write 4 as 22
2a+b = (22)c-d   Now apply rule 3 to the right-hand side
2a+b = 22(c-d)   Since we have the same base on both sides (i.e. 2), and the right-hand side equals the left-hand side, we know that the exponents must be equal

Therefore, a + b = 2(c - d) This is the relationship between a, b, c and d

Cheers,

Leeanne

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