Question

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

5 to the fourth power, over 25 = 52

A:By simplifying 25 to 52 to make both powers base five, and subtracting the exponents
B:By simplifying 25 to 52 to make both powers base five, and adding the exponents
C:By finding the quotient of the bases to be one fifth, and cancelling common factors
D:By finding the quotient of the bases to be one fifth, and simplifying the expression

Answer 1

`\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^(-n) \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^(-n)} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^(-m)\implies a^(n-m) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{5^4}{25}=5^2~\hfill \cfrac{5^4}{5^2}\implies 5^4\cdot 5^(-2)\implies 5^(4-2)\implies 5^2`

Answer 2

c.

Explanation:

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