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      • PROPERTIES OF EXPONENTS

      PROPERTIES OF EXPONENTS

      • Posted by Ramachandran
      • Categories Exponents
      • Date 14th January 2020
      • Comments 0 comment

      In this section, we will learn the properties of exponents. We have listed the properties of exponents.

      xm ⋅ xn  =  x(m + n) If two or more terms are multiplying with the same base, we may write only one base and add the powers.
      xm  / xn  =  x(m – n) If two terms are dividing with the same base, we may
      write only one base and subtract the powers.
      (xm)n  =  xmn If we have power raised to another power, then
      we should multiply both the powers
      x-m  =  1/xm (or) (a/b)-m  =  (b/a)m If we have negative exponent, then we can write the reciprocal form of the given number to make the negative exponent as positive.
      x0  =  1The value of anything to the power will be 1

      Example problems on properties of exponents

      Example 1 :

      Simplify

      2m2 ⋅ 3m3

      Solution :

      2m2 ⋅ 3m3 =  6m(2 + 3)

      2m2 ⋅ 3m3 = 6m5

      Example 2 :

      Simplify

      Solution :

      (2x3/y3) ⋅ (x4/ y2) =  2x(3 + 4) / y(3 + 2)

      =  2x7 / y5

      Example 3 :

      Simplify

      Solution :

      = 4g-4 b4 ⋅ 2gb-5

      = 8g(-4 + 1) b(4 – 5)

      = 8g-3 b– 1

      = 8/g3b

      Example 4 :

      Simplify

      Solution :

      For all the terms, we have same base. So, we can write only one base and add the powers.

      = (6/7)(4 + 2 + 3)

        =  (6/7)9

      Related Pages

      • Exponents and Radicals
      • Write the given expression in exponential form

      • Share:
      Ramachandran

      Previous post

      EXPONENTS AND RADICALS
      14th January 2020

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