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edwin.que
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Let k = 10^10. Then K is 1 followed by 10 zeros. The number k is 1 fol Updated on: 13 Apr 2024, 12:28
Originally posted by edwin.que on 29 Oct 2023, 18:49.
Last edited by Bunuel on 13 Apr 2024, 12:28, edited 3 times in total.
Corrected typographical error and formatted the question
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68% (01:31) correct 32% (01:46) wrong based on 985 sessions

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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. \(10^{20}\)­


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D
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MartyMurray
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Let k = 10^10. Then K is 1 followed by 10 zeros. The number k is 1 fol 29 Oct 2023, 20:38
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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).
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Let k = 10^10. Then K is 1 followed by 10 zeros. The number k is 1 fol 29 Oct 2023, 22:17
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edwin.que
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. \(10^{20}\)
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\(k = 10^{10}\)

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

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

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

Option D
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sachi-in
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Let k = 10^10. Then K is 1 followed by 10 zeros. The number k is 1 fol 23 Dec 2023, 23:34
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edwin.que
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. \(10^{20}\)
Show more


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 )
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Let k = 10^10. Then K is 1 followed by 10 zeros. The number k is 1 fol 02 Nov 2024, 07:23
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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}}[/m] equal to 10^{{11} ?
MartyMurray
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).
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Bunuel
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Let k = 10^10. Then K is 1 followed by 10 zeros. The number k is 1 fol 02 Nov 2024, 09:52
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slabarca
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}}[/m] equal to 10^{{11} ?
MartyMurray
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).
Show more

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

Thus:

\(10^{10 * 10^{10}} = 10^{(10 * 10^{10})} = 10^{({10}^{1+10})} =10^{{10}^{11}}\)
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Let k = 10^10. Then K is 1 followed by 10 zeros. The number k is 1 fol 01 Dec 2024, 20:05
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KarishmaB - it's more trickier than it's difficult. Any suggestions on similar questions?
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ManishaPrepMinds
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Let k = 10^10. Then K is 1 followed by 10 zeros. The number k is 1 fol 11 Nov 2025, 02:19
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  • 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
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