Simplify the Expression: b⁵/b² Using Exponent Rules

Insert the corresponding expression:

$\frac{b^5}{b^2}=$

Video Solution

Solution Steps

00:00 Simply

00:04 According to the laws of exponents, division of powers with equal bases (A)

00:08 equals the same base (A) raised to the power of the difference of exponents (M-N)

00:11 We'll use this formula in our exercise

00:16 We'll compare term by term according to the formula and simplify

00:23 We'll keep the base

00:29 We'll subtract between the exponents

00:43 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we need to simplify the expression $\frac{b^5}{b^2}$ using the rules of exponents.

Step 1: Identify the rule to apply: For any positive integer exponents $m$ and $n$ , the rule $\frac{a^m}{a^n} = a^{m-n}$ applies when dividing terms with the same base. In this expression, our base is $b$ .
Step 2: Apply the rule: Substitute the given exponents into the formula: $\frac{b^5}{b^2} = b^{5-2}$
Step 3: Perform the subtraction: Calculate the exponent $5 - 2$ : $b^{5-2} = b^3$

Therefore, the solution to the expression $\frac{b^5}{b^2}$ is $b^3$ .