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
00:02 We'll use the formula for dividing powers
00:04 Any division of powers with the same base (A) and different exponents
00:07 Equals the same base (A) raised to the difference of the exponents (M-N)
00:10 We'll use this formula in our exercise
00:13 And we'll compare the numbers to the variables in the formula
00:32 We'll keep the base and subtract between the powers
00:51 We'll calculate the difference
00:56 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