Simplify 7^4 × 7: Power Multiplication Problem

Question

Simplify the following equation:

$7^4\times7=$

00:00 Simplify the following problem

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

00:06 We'll apply this formula to our exercise, and raise to the power of 1

00:13 According to the laws of exponents, the multiplication of powers with the same base (A)

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

00:22 We'll apply this formula to our exercise

00:23 We'll then proceed to add up the exponents and raise them to this power

00:29 This is the solution

To simplify the expression $7^4 \times 7$ , we follow these steps:

Step 1: Recognize that $7$ is equivalent to $7^1$ . Thus, our expression becomes $7^4 \times 7^1$ .
Step 2: Apply the rule of multiplying powers with the same base, which states: $a^m \times a^n = a^{m+n}$ .
Step 3: According to the rule, add the exponents of the same base: $4 + 1$ .
Step 4: Simplify the result, yielding $7^{4+1} = 7^5$ .

Thus, the simplified expression is $7^5$ .

$7^5$