Simplify Powers: 15^2 × 15^4 Using Exponent Properties

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 According to the laws of exponents, multiplying exponents with the same base (A)

00:06 is equal to the same base raised to the sum of the exponents (N+M)

00:10 We will apply this formula to our exercise

00:13 We'll add up the exponents and raise them to this power

00:19 This is the solution

Step-by-Step Solution

To solve the problem of simplifying $15^2 \times 15^4$ , we will use the rule for multiplying exponents with the same base.

According to the multiplication of powers rule: If $a$ is a real number and $m$ and $n$ are integers, then:

$a^m \times a^n = a^{m+n}$ .

Applying this rule to our problem, where the base $a$ is 15, and the exponents $m$ and $n$ are 2 and 4 respectively:

Step 1: Identify the base and exponents: $15^2$ and $15^4$ have the same base.
Step 2: Add the exponents: $2 + 4 = 6$ .
Step 3: Simplify the expression using the rule: $15^2 \times 15^4 = 15^{2+4} = 15^6$ .

Therefore, the simplified expression is $15^6$ .