Advertisements
Advertisements
प्रश्न
If \[\sqrt{5^n} = 125\] then `5nsqrt64`=
पर्याय
25
\[\frac{1}{125}\]
625
\[\frac{1}{5}\]
Advertisements
उत्तर
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
संबंधित प्रश्न
Simplify the following:
`(5^(n+3)-6xx5^(n+1))/(9xx5^x-2^2xx5^n)`
Assuming that x, y, z are positive real numbers, simplify the following:
`sqrt(x^3y^-2)`
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrtx)^((-2)/3)sqrt(y^4)divsqrt(xy^((-1)/2))`
Simplify:
`root5((32)^-3)`
Show that:
`(x^(a-b))^(a+b)(x^(b-c))^(b+c)(x^(c-a))^(c+a)=1`
Find the value of x in the following:
`(2^3)^4=(2^2)^x`
Solve the following equation:
`8^(x+1)=16^(y+2)` and, `(1/2)^(3+x)=(1/4)^(3y)`
The value of x − yx-y when x = 2 and y = −2 is
The seventh root of x divided by the eighth root of x is
If x = \[\frac{2}{3 + \sqrt{7}}\],then (x−3)2 =
