Question

Explain how the Quotient of Powers Property was used to simplify this expression.

Answer 1

Answer:

$\frac{5^{4}}{25} = 25$

Step-by-step explanation:

I'm not sure if you had a typographical error with this statement, "5 to the fourth power, over 25 = 52."

According to the Quotient Rule of Exponents:

$\frac{a^{m}}{a^{n}} = a^{(m-n)}$

Method 1:

In order for you apply the Quotient Rule, the base must be the same. Since 5 is a factor of 25, then you could rewrite 25 as 5². Doing so will give you the following exponential expression:

$\frac{5^{4}}{5^{2}} = 5^{(4 - 2)} = 5^{2} = 25$

Method 2:

Even if you solve the given problem manually, you'd still get the same answer:

$\frac{5^{4}}{25} = \frac{5*5*5*5}{25} = \frac{625}{25} = 25$

Both methods produced the same result, proving that the correct answer is 25.

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