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

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

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Step-by-step video solution

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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 written solution

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1

Understand the problem

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

2

Step-by-step solution

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

Here, we have 5654=56−4 \frac{5^6}{5^4} = 5^{6-4} . Simplifying, we get 52 5^2 .

3

Final Answer

52 5^2

Practice Quiz

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\( 112^0=\text{?} \)

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