Grades 11-12 Video Solutions 2023-2023_11-12

Video Transcription

Problem number 17. The number 5 to the power of 5 to the power of 6 can be written in the form n to the power of n for some integer n. What is the value of  n? Okay, so first we're going to write the exponent 5 to the power of 6 as 5 times 5 to the power of 5. So we're just taking one 5 from the exponent and just  multiplying the 5 by it instead of having it in the exponent. But now we see so many 5's. In fact, we can even rewrite this as 5 to the power of 5 to the power  of 5 to the power of 5. And we can see now that if n is equal to 5 to the power of 5, we have this number can be written as n to the power of n when n is equal  to 5 to the power of 5. And that gives us our answer of C.

Video Summary

Problem number 17. The number 5 to the power of 5 to the power of 6 can be written in the form n to the power of n for some integer n. What is the value of n? Okay, so first we're going to write the exponent 5 to the power of 6 as 5 times 5 to the power of 5. So we're just taking one 5 from the exponent and just multiplying the 5 by it instead of having it in the exponent. But now we see so many 5's. In fact, we can even rewrite this as 5 to the power of 5 to the power of 5 to the power of 5. And we can see now that if n is equal to 5 to the power of 5, we have this number can be written as n to the power of n when n is equal to 5 to the power of 5. And that gives us our answer of C.

Keywords

power

exponentiation

integer

mathematics

problem-solving