Solve 5^6 ÷ 5^4: Division of Powers with Same Base

Question

5654= \frac{5^6}{5^4}=

Video Solution

Solution Steps

00:00 Simply
00:03 According to the laws of exponents, division of powers with equal bases (A)
00:07 equals the same base (A) raised to the difference of exponents (M-N)
00:11 Let's use this formula in our exercise
00:15 Let's compare terms according to the formula and simplify
00:26 Keep the base
00:34 Subtract between the exponents
00:44 Calculate the difference of exponents
00:54 And this is the solution to the question

Step-by-Step Solution

Using the quotient rule for exponents: aman=amn \frac{a^m}{a^n} = a^{m-n} .

Here, we have 5654=564 \frac{5^6}{5^4} = 5^{6-4} . Simplifying, we get 52 5^2 .

Answer

52 5^2