Calculate (12×3)^5: Evaluating the Fifth Power of a Product

Question

Insert the corresponding expression:

(12×3)5= \left(12\times3\right)^5=

Video Solution

Solution Steps

00:00 Simply
00:03 To open parentheses of power over multiplication
00:06 Raise each factor to the power
00:13 We will use this formula in our exercise
00:20 And this is the solution to the question

Step-by-Step Solution

The given expression is (12×3)5 (12 \times 3)^5 . According to the Power of a Product rule, which states that (a×b)n=an×bn(a \times b)^n = a^n \times b^n, we apply this formula to the expression.


  • Firstly, identify the base of the power as the product 12×312 \times 3.
  • Secondly, recognize that the exponent applied to this product is 5.
  • According to the rule, the power of a product can be distributed to each factor in the product, which means: (12×3)5=125×35(12 \times 3)^5 = 12^5 \times 3^5.

Therefore, the expression (12×3)5 (12 \times 3)^5 corresponds to 125×35 12^5 \times 3^5 .

Answer

125×35 12^5\times3^5