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Raising A Product To A Power
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 VariableA
^{P}
× VariableB
^{P}
.
A real example: (5 × 3)
^{2}
equals (15)
^{2}
= 225. Or looked at another way: (5 × 3)
^{2}
equals 5
^{2}
× 3
^{2}
= 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}
6
^{3}
= 2
^{3}
× 3
^{3}
= 8 × 27 = 216
No
(5 + 4)
^{2}
(9)
^{2}
= 81
No
(5 - 4)
^{2}
(1)
^{2}
= 1
See More About Roots Of Numbers