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

Question

Choose the expression that corresponds to the following:

(12×3)5= \left(12\times3\right)^5=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 In order to expand parentheses containing a multiplication operation with an outside exponent
00:06 Raise each factor to the power
00:13 We will apply this formula to our exercise
00:20 This is the solution

Step-by-Step Solution

The given expression is (12×3)5 (12 \times 3)^5 . The power of a product rule states that (a×b)n=an×bn(a \times b)^n = a^n \times b^n. We will 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