Simplify Powers of 15: Solving 15^4 × 15 × 15^3

Question

Simplify the following equation:

$15^4\times15\times15^3=$

00:00 Simplify the following problem

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

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

00:13 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 will apply this formula to our exercise

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

00:41 This is the solution

To solve this problem, we'll employ the multiplication rule for exponents:

Step 1: Convert $15$ into exponential form: $15 = 15^1$ .
Step 2: Apply the exponent rule to the expression $15^4 \times 15 \times 15^3$ .
Step 3: Simplify by adding the exponents: $15^4 \times 15^1 \times 15^3 = 15^{4+1+3}$ .
Step 4: Perform the addition: $4 + 1 + 3 = 8$ .

Therefore, the simplified form of the expression is $15^8$ .

The correct answer matches choice 3, which is: $15^8$ .

$15^8$