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Math K-Plus

Exponents - Learn About Raising A Product To A Power

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Explain Raising A Product To A Power


Before we move forward and learn about Raising A Product To A Power, be sure you understand the basics. Recommended reading: Exponents.
  • An abstract example of raising products to a power is the following:
    (VariableA × VariableB)Raised Power Exponent (P) equals VariableAP × VariableBP.
    A real example: (5 × 3)2 equals (15)2 = 225. Or looked at another way: (5 × 3)2 equals 52 × 32 = 9 × 25 = 225.
  • There is no way to combine the sum of two powers with the same base into one expression: (3 + 3)2 can not be combined.
    However, the answer can be simplified: (9)2 equals 81. The same approach apply's to this variation of the problem: (3 + 2)2 equals (5)2 equals 25.
  • There is no way to combine the difference of two powers with the same base into one expression: (5 - 5)2 can not be combined.
    However, the answer can be simplified: (0)2 equals 0. The same approach apply's to this variation of the problem: (3 - 2)2 equals (1)2 equals 1.

Syntax Example

Expression Can Be Combined?


Math Expression


Answer


Yes (2 × 3)3 63 = 23 × 33 = 8 × 27 = 216
No (5 + 4)2 (9)2 = 81
No (5 - 4)2 (1)2 = 1