Simplify 5^(-2) × 5^(-1) × 5: Negative Exponent Reduction

Reduce the following equation:

$5^{-2}\times5^{-1}\times5=$

Video Solution

Solution Steps

00:00 Simplify the following problem

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

00:07 We will 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 equal bases (A)

00:18 equals the same base raised to the power of the sum of the exponents (N+M)

00:22 We will apply this formula to our exercise

00:27 Note that we are adding a negative factor

00:41 A positive x A negative is always negative, therefore we subtract as follows

00:48 This is the solution

Step-by-Step Solution

To solve this problem, we'll apply the rule for multiplying powers with the same base:

Step 1: Identify the expression given, $5^{-2}\times5^{-1}\times5$ .
Step 2: Notice that all terms are powers of 5. Therefore, we can add their exponents.
Step 3: The exponents are -2 for $5^{-2}$ , -1 for $5^{-1}$ , and 1 for $5$ .

Let's perform the required calculations:

$-2 + (-1) + 1 = -2$

Using the power rule, the expression simplifies to:

$5^{-2} = 5^{-2}$

Therefore, the reduced form of the equation $5^{-2}\times5^{-1}\times5$ is $5^{-2}$ .