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# (1/1)/(1/5^(-2))

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Math Expert
Joined: 02 Sep 2009
Posts: 58443

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26 Aug 2018, 05:45
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Difficulty:

15% (low)

Question Stats:

89% (00:25) correct 11% (00:34) wrong based on 25 sessions

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$$\frac{\frac{1}{1}}{\frac{1}{5^{-2}}}$$is equal to which of the following?

(A) $$\frac{1}{25}$$

(B) $$\frac{1}{5}$$

(C) $$1$$

(D) $$5$$

(E) $$25$$

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26 Aug 2018, 08:25
Bunuel wrote:
$$\frac{\frac{1}{1}}{\frac{1}{5^{-2}}}$$is equal to which of the following?

(A) $$\frac{1}{25}$$

(B) $$\frac{1}{5}$$

(C) $$1$$

(D) $$5$$

(E) $$25$$

$$\frac{\frac{1}{1}}{\frac{1}{5^{-2}}}$$

$$= \frac{1}{1}/25$$

Now, $$\frac{1}{1} = 1$$ , So we are left we $$\frac{1}{25}$$ , Answer must be (A)
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26 Aug 2018, 08:53
Bunuel wrote:
$$\frac{\frac{1}{1}}{\frac{1}{5^{-2}}}$$is equal to which of the following?

(A) $$\frac{1}{25}$$

(B) $$\frac{1}{5}$$

(C) $$1$$

(D) $$5$$

(E) $$25$$

Numerator of the given expression: $$\frac{1}{1}$$=1
Numerator of the given expression:$$\frac{1}{5^{-2}}$$=$$(5^{-2})^{-1}=5^{(-2)*(-1)}=5^2=25$$

So, given expression is simplified to:- $$\frac{Numerator}{Denominator}$$=$$\frac{1}{25}$$

Properties of exponents used to simplify denominator:-
a) $$\frac{1}{a^m}$$=$$a^{-m}$$
b) $$(a^m)^n=a^{m*n}$$
I hope everybody knows these, still I reminded.

Ans. (A)
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Joined: 31 Oct 2013
Posts: 1465
Concentration: Accounting, Finance
GPA: 3.68
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26 Aug 2018, 11:22
Bunuel wrote:
$$\frac{\frac{1}{1}}{\frac{1}{5^{-2}}}$$is equal to which of the following?

(A) $$\frac{1}{25}$$

(B) $$\frac{1}{5}$$

(C) $$1$$

(D) $$5$$

(E) $$25$$

$$\frac{1}{1}$$ = 1

$$\frac{1}{1/ 5^{-2}}$$

= $$\frac{1}{1/ 1 / 25}$$

= 25

So, 1 / 25.

Re: (1/1)/(1/5^(-2))   [#permalink] 26 Aug 2018, 11:22
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