Math

QuestionSimplify 2365÷233223^{65} \div 23^{32} using the Quotient Rule of Integer Exponents.

Studdy Solution

STEP 1

Assumptions1. We are given two expressions with the same base (23) raised to different powers (65 and32). . We are asked to simplify the expression using the Quotient Rule of Integer Exponents.

STEP 2

The Quotient Rule of Integer Exponents states that for any non-zero number 'a' and integers 'm' and 'n', the expression am÷ana^m \div a^n can be simplified to amna^{m-n}.
am÷an=amna^m \div a^n = a^{m-n}

STEP 3

Now, let's apply this rule to our given expression 2365÷233223^{65} \div23^{32}.
2365÷2332=23653223^{65} \div23^{32} =23^{65-32}

STEP 4

Subtract the exponents.
236532=233323^{65-32} =23^{33}So, 2365÷233223^{65} \div23^{32} simplifies to 233323^{33}.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord