To analyze how the Quotient of Powers Property was used to simplify the expression \( \frac{5^4}{25} = 5^2 \), let's break down the options given:
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Understanding the expression: The expression \( \frac{5^4}{25} \) can be rewritten because \( 25 \) is \( 5^2 \). Therefore, we have: \[ \frac{5^4}{25} = \frac{5^4}{5^2} \]
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Applying the Quotient of Powers Property: The Quotient of Powers Property states that when dividing powers with the same base, you subtract the exponents. In this case: \[ \frac{5^4}{5^2} = 5^{4-2} = 5^2 \]
Now, looking at the choices given:
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a) By simplifying 25 to 52 to make both powers base five and subtracting the exponents: This statement is correct because it explains that you rewrite \( 25 \) as \( 5^2 \) and then apply the property correctly by subtracting exponents.
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b) By simplifying 25 to 52 to make both powers base five and adding the exponents: This is incorrect because you subtract the exponents, not add them.
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c) By finding the quotient of the bases to be one fifth and cancelling common factors: This is not how the Quotient of Powers Property is applied here, so it does not explain the simplification accurately.
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d) By finding the quotient of the bases to be one fifth and simplifying the expression: This implies a method not used here, as we didn't directly find the quotient of different bases.
From this analysis, the best answer is a) because it correctly explains the process of simplification as applied in this expression.
1 answer