Simplify 60^60 ÷ 60^42: Power Division Problem

Question

Insert the corresponding expression:

60606042= \frac{60^{60}}{60^{42}}=

Video Solution

Solution Steps

00:00 Solve
00:03 According to the laws of exponents, division of exponents with equal bases (A)
00:06 equals the same base (A) raised to the power of the difference of exponents (M-N)
00:09 Let's use this formula in our exercise
00:12 We'll keep the base and subtract between the exponents
00:15 And this is the solution to the question

Step-by-Step Solution

To solve the expression 60606042 \frac{60^{60}}{60^{42}} , we need to apply the Power of a Quotient Rule for Exponents. This rule states that when dividing like bases, we subtract the exponents. In mathematical terms, for any non-zero number a a , and integers m m and n n , aman=amn \frac{a^m}{a^n} = a^{m-n} .

Applying this rule to our problem:

  • We have the same base:60 60 .

  • We subtract the exponent in the denominator from the exponent in the numerator: 606042 60^{60-42} .

  • This simplifies the expression to 6018 60^{18} .

Therefore, the solution to the question is: 6018 60^{18} .

Answer

6018 60^{18}