Simplify Powers of 6: 6²×6⁵×6 Multiplication Problem

Question

Simplify the following equation:

$6^2\times6^5\times6=$

00:00 Simplify the following problem

00:03 Any number raised to the power of 1 is always equal to itself

00:08 We'll apply this formula to our exercise, and raise it to the power of 1

00:12 According to the laws of exponents, the multiplication of powers with an equal base (A)

00:17 equals the same base raised to the sum of the exponents (N+M)

00:21 We'll apply this formula to our exercise

00:25 We'll maintain the base and add together the exponents

00:35 This is the solution

To simplify the expression $6^2 \times 6^5 \times 6$ , we apply the rules of exponents because all terms have the same base.

Identify each power: $6^2$ , $6^5$ , and $6$ . Remember that $6$ is equivalent to $6^1$ .
Using the exponent multiplication rule: $a^m \times a^n = a^{m+n}$ .
Combine the exponents: $6^{2+5+1}$ .
Calculate the sum of the exponents: $2 + 5 + 1 = 8$ .

Therefore, the solution to the problem is $\boxed{6^8}$ .

$6^8$