Which of the following are equal to (1/560)^(−4)?

Question

Which of the following are equal to  (\frac{1}{560})^{(-4)} ?

I.  \frac{(560^5 - 560^4)}{559}

II.  \frac{560^{(-8)}}{560^2}

III.  70^4*(\frac{1}{8})^{(-4)}

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

Archit3110 · Answer

given

(\frac{1}{560})^{(-4)} 
i.e = 560^4
IMO option I & III are correct
IMO D

LevanKhukhunashvili · Answer

(\frac{1}{560})^{(-4)} = 560^4=2^16*5^4*7^4

I. 560^4*(560-1)/559=560^4; Valid
II. 1/ 560^8 *1/ 560^2 =1/ 560^10 ; Not Valid
III.  2^4*5^4*7^4*2^12=2^16*5^4*7^4

IMO
Ans:  D

LeoN88 · Answer

II is 560^(-10)

I & III are 560^4

saynchalk · Answer

someone explain option 3 please, and also, is it raised to -4 or multiplied by -4 in the third option

Krunaal · Answer

(\frac{1}{560})^{(-4)}  =  560^4

Option 3:   70^4*(\frac{1}{8})^{(-4)}

=  70^4 * 8^4

=  (70*8)^4 = 560^4

Option 1:   \frac{(560^5 - 560^4)}{559}

=  \frac{(560^4 * (560 - 1))}{559}

=  560^4

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