Let k = 10^10. Then K is 1 followed by 10 zeros. The number k is 1 fol

Question

Let k = 10^{10} . Then k is 1 followed by 10 zeros. The number k^k is 1 followed by how many zeros? A. 20 B. 100 C. 10^{10} D. 10^{11} E. 10^{20} https://gmatclub.com/forum/download/file.php?id=81457 GMAT-Club-Forum-thyzn0g9.png

MartyMurray · Accepted Answer

Let  k = 10^{10} . Then  k  is  1  followed by  10  zeros. The number  k^k  is  1  followed by how many zeros?

A.  20 
B.  100 
C.  10^{10} 
D.  10^{11} 
E.  10^{20}

k^k = (10^{10})^{10^{10}}

When we raise a number with an exponent to a power, we multiply the exponents.

So,  k^k = 10^{10 x 10^{10}} = 10^{{10}^{11}} .

Therefore,  k^k  is  1  followed by  10^{11}  zeros.

The correct answer is (D).

gmatophobia · Answer

k = 10^{10}

k^k = 10^{10^{(10^{10})}}

k^k = 10^{(10 * 10^{10})}

k^k = 10^{(10^{11})}

Option D

sachi-in · Answer

Using Logarithm base 10 is easier for 10 powers since 
log(10) = 1 = 2 digit ( 1 zero )
log(100) = 2 = 3 digits ( 2 zeros )

log(k) = 10 log 10 = 10
log (k^k) = (k) * (log k) = (10^10) * (10) = 10^11 ( THIS MANY ZEROES )

slabarca · Answer

Hello Marty, I still don't get how you do your last step; where you get

"  k^k = 10^{10 x 10^{10}} = 10^{{10}^{11}} ."

Why is 10^{{10}^{11}}  equal to 10^{{11} ?

Bunuel · Answer

a^{m^n} = a^{(m^n)}

Thus:

10^{10 * 10^{10}} = 10^{(10 * 10^{10})} = 10^{({10}^{1+10})} =10^{{10}^{11}}

MBAToronto2024 · Answer

KarishmaB  - it's more trickier than it's difficult. Any suggestions on similar questions?

ManishaPrepMinds · Answer

k = 10^10 means k is 1 with 10 zeros → k = 10,000,000,000 
 k^k = (10^10)^(10^10) = 10^(10 × 10^10) = 10^(10^11) 
 So k^k is 1 with 10^11 zeros

KarishmaB · Answer

Responding to a pm:

Focus on the exponent rules and just simplify.

k = 10^{10}

k^k = (10^{10})^{10^{10}}=10^{10*10^{10}}= 10^{10^{11}}

Now go back to the question:
 10^{10}  converts to '1 followed by 10 zeroes'. So
 10^{10^{11}}  converts to '1 followed by 10^11 zeroes.

Answer (D)

Let k = 10^10. Then K is 1 followed by 10 zeros. The number k is 1 fol

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Let k = 10^10. Then K is 1 followed by 10 zeros. The number k is 1 fol

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