Pre-Algebra Fractional Exponent QuestionWhy does t 3 2 ⋅ t 1 2 = t 2 ?What I tried to do was multiply the exponents together 3 2 ⋅ 1 2 = 3 4 so my final answer was t 3 4 but according to my Wileyplus homework it is t 2 .Can someone please explain?

Question

Pre-Algebra Fractional Exponent QuestionWhy does       t                  3        2              ⋅      t                  1        2              =      t    2  ?What I tried to do was multiply the exponents together       3    2    ⋅      1    2    =      3    4   so my final answer was       t                  3        4             but according to my Wileyplus homework it is       t    2  .Can someone please explain?

lodosr · Accepted Answer

When multiplying two of the same number raised to exponents (such as             x              3        2             times       x                  1        2            ) you add the exponents.      x    a    ⋅      x    b    =      x          a      +      b      Only when raising a number to an exponent, and raising the result to an exponent do you multiply exponents together.  (      x    a        )    b    =      x          a      ⋅      b      Note:   (      x          a            )          b        ≠      x          (              a        b            )

flightwingsd2 · Accepted Answer

Just remember this:      a    b    +      a    c    =      a          b      +      c      so in your problem,  a  =  t  ,    b  =  3      /    2  ,    c  =  1      /    2and      t    3        /    2  +      t    1        /    2  =      t          1              /            2      +      3              /            2        =      t    4        /    2  =      t    2  hope this helped!