Calculate (2×4×6×3)^5: Product and Power Expression

Question

Insert the corresponding expression:

(2×4×6×3)5= \left(2\times4\times6\times3\right)^5=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:04 According to the laws of exponents, a product raised to a power (N)
00:08 Equals a product where each factor is raised to the same power (N)
00:13 This formula is valid regardless of how many factors are in the product
00:24 We will apply this formula to our exercise
00:28 We'll break down the product into each factor separately raised to the power (N)
00:36 This is the solution

Step-by-Step Solution

To solve the problem (2×4×6×3)5 \left(2 \times 4 \times 6 \times 3\right)^5 , we will apply the power of a product rule.

Step 1: Identify the expression inside the parenthesis:
We have 22, 44, 66, and 33 as factors, so the expression is 2×4×6×32 \times 4 \times 6 \times 3.

Step 2: Apply the power of a product rule:
According to the rule, (a×b×c×d)n=an×bn×cn×dn(a \times b \times c \times d)^n = a^n \times b^n \times c^n \times d^n.

Using this rule, the expression becomes:
25×45×65×352^5 \times 4^5 \times 6^5 \times 3^5.

Therefore, the expression that represents (2×4×6×3)5\left(2 \times 4 \times 6 \times 3\right)^5 is 25×45×65×352^5 \times 4^5 \times 6^5 \times 3^5.

Answer

25×45×65×35 2^5\times4^5\times6^5\times3^5