Simplify the Exponential Expression: 5³÷5⁸

Question

Insert the corresponding expression:

5358= \frac{5^3}{5^8}=

Video Solution

Solution Steps

00:07 Let's get started.
00:09 We're going to explore dividing powers.
00:12 If you have A raised to the power of N,
00:16 divided by A raised to the power of M,
00:20 it equals A raised to the power of M minus N.
00:24 We'll use this rule in our practice problem.
00:27 And there you have it, that's the solution!

Step-by-Step Solution

We need to simplify the expression 5358 \frac{5^3}{5^8} using the rules of exponents. Specifically, we will use the power of a quotient rule for exponents which states that when you divide like bases you subtract the exponents:

aman=am−n \frac{a^m}{a^n} = a^{m-n} .

Here, the base is 5, the exponent in the numerator is 3, and the exponent in the denominator is 8.

  • Apply the rule: 53−8 5^{3-8}
  • Subtract the exponents: 5−5 5^{-5} .

Therefore, the simplified expression is 5−5 5^{-5} .

The solution to the question is: 5−5 5^{-5}

Answer

5−5 5^{-5}

More Questions

Related Subjects

Division of Exponents with the Same Base

Question Types

Power of a Quotient Rule for Exponents: Applying the formula Power of a Quotient Rule for Exponents: Calculating powers with negative exponents