How to Solve Exponents

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How to Solve Exponents

Image Credits: Pinterest.

Exponents are used when a number is multiplied by itself. You can also easily add, subtract, and multiply exponents for simplifying problems as needed when you have learned the property rules. Here is how to solve exponents. 

How to Solve Basic Exponents

Multiply the base repeatedly for the number of factors represented by the exponent.

 82 = 8 × 8 = 64
–  53 = 5 × 5 × 5 = 125
45 = 4 × 4 × 4 × 4 × 4 = 1024

How to Add or Subtract Exponents with the Same Base and Exponent

You can only add or subtract exponents if they have the same identical bases and exponents. 

  • \mathbf{\2^{3} + 2^{3} = 1 *2^{3} + 1* 2^{3} = 2 * 2^{3} = 2 * 8 = 16}
  • \mathbf{3^{2}-3^{2}+5=5}
  • \mathbf{6x^{2}-3x^{2}=3x^{2}}

How to Solve Exponents with the Properties

  1. The product of powers property tells that when you multiply powers with the same base you just have to add the exponents.

    \boldsymbol{\mathbf{}x^{a} + x^{b} = x^{a+b}}

    For Example,  \mathbf{x^{2} + x^{3} = (x.x) + (x.x.x) = x^{5}}

  2.  The power of a power property says that to find a power of a power you just have to multiply the exponents.

    \mathbf{(x^{a})^{b}} = \mathbf{x^{ab}}

    For Example, \mathbf{(x^{2})^{5} = x^{2*5} = x^{10}}

  3. The power of a product property says when you raise a product to a power you raise each factor with a power. 

    \mathbf{(xy)^{a} = x^{a}y^{a} } 

    For Example,