Advertisements
Advertisements
Question
If \[\sqrt{5^n} = 125\] then `5nsqrt64`=
Options
25
\[\frac{1}{125}\]
625
\[\frac{1}{5}\]
Advertisements
Solution
We have to find `5nsqrt64` provided \[\sqrt{5^n} = 125\]
So,
`sqrt 5^n = 125`
`5^(nxx 1/2)= 5^3`
`n/2 = 3`
`n=3xx2`
` n =6`
Substitute ` n =6` in `5nsqrt64` to get
` `5nsqrt64 = 5^(2^(6x1/6)`
=` 5^(2^(6x1/6)`
`= 5xx5`
`=25`
Hence the value of `5nsqrt64` is 25.
APPEARS IN
RELATED QUESTIONS
Simplify the following
`3(a^4b^3)^10xx5(a^2b^2)^3`
Prove that:
`1/(1+x^(a-b))+1/(1+x^(b-a))=1`
Solve the following equation for x:
`2^(5x+3)=8^(x+3)`
Find the value of x in the following:
`2^(x-7)xx5^(x-4)=1250`
If `2^x xx3^yxx5^z=2160,` find x, y and z. Hence, compute the value of `3^x xx2^-yxx5^-z.`
Write the value of \[\sqrt[3]{125 \times 27}\].
The value of \[\left\{ 2 - 3 (2 - 3 )^3 \right\}^3\] is
Which one of the following is not equal to \[\left( \frac{100}{9} \right)^{- 3/2}\]?
If \[2^{- m} \times \frac{1}{2^m} = \frac{1}{4},\] then \[\frac{1}{14}\left\{ ( 4^m )^{1/2} + \left( \frac{1}{5^m} \right)^{- 1} \right\}\] is equal to
If x= \[\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}\] and y = \[\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}\] , then x2 + y +y2 =
