Advertisements
Advertisements
प्रश्न
Simplify:
`((5^-1xx7^2)/(5^2xx7^-4))^(7/2)xx((5^-2xx7^3)/(5^3xx7^-5))^(-5/2)`
Advertisements
उत्तर
Given `((5^-1xx7^2)/(5^2xx7^-4))^(7/2)xx((5^-2xx7^3)/(5^3xx7^-5))^(-5/2)`
`((5^-1xx7^2)/(5^2xx7^-4))^(7/2)xx((5^-2xx7^3)/(5^3xx7^-5))^(-5/2)=((5^(-1xx7/2)xx7^(2xx7/2))/(5^(2xx7/2)xx7^(-4xx7/2)))xx((5^(-2xx(-5)/2)xx7^(3xx(-5)/2))/(5^(3xx(-5)/2)xx7^(-5xx(-5)/2)))`
`rArr((5^-1xx7^2)/(5^2xx7^-4))^(7/2)xx((5^-2xx7^3)/(5^3xx7^-5))^(-5/2)=(5^((-7)/2)xx7^7)/(5^7xx7^-14)xx(5^5xx7^((-15)/2))/(5^((-15)/2)xx7^(25/2))`
By using the law of rational exponents `a^m/a^n=a^(m-n)` we have
`rArr((5^-1xx7^2)/(5^2xx7^-4))^(7/2)xx((5^-2xx7^3)/(5^3xx7^-5))^(-5/2)=(5^((-7)/2)xx7^7)/(5^7xx7^-14)xx(5^5xx7^((-15)/2))/(5^((-15)/2)xx7^(25/2))`
`=5^((-7)/2-7)xx7^(7+14)xx5^(5+15/2)xx7^(-15/2-25/2)`
`=5^((-7)/2-14/2)xx7^21xx5^(10/2+15/2)xx7^(-40/2)`
`=5^(-7/2-14/2+10/2+15/2)xx7^(21-40/2)`
`=5^((-7-14+10+15)/2)xx7^((42-40)/2)`
`=5^(4/2)xx7^(2/2)`
`=5^2xx7^1`
`=25xx7`
= 175
Hence the value of `((5^-1xx7^2)/(5^2xx7^-4))^(7/2)xx((5^-2xx7^3)/(5^3xx7^-5))^(-5/2)` is 175
APPEARS IN
संबंधित प्रश्न
Simplify the following
`((x^2y^2)/(a^2b^3))^n`
Solve the following equations for x:
`2^(2x)-2^(x+3)+2^4=0`
Find the value of x in the following:
`(2^3)^4=(2^2)^x`
Solve the following equation:
`4^(x-1)xx(0.5)^(3-2x)=(1/8)^x`
Solve the following equation:
`sqrt(a/b)=(b/a)^(1-2x),` where a and b are distinct primes.
If 1176 = `2^axx3^bxx7^c,` find the values of a, b and c. Hence, compute the value of `2^axx3^bxx7^-c` as a fraction.
Show that:
`((a+1/b)^mxx(a-1/b)^n)/((b+1/a)^mxx(b-1/a)^n)=(a/b)^(m+n)`
The simplest rationalising factor of \[2\sqrt{5}-\]\[\sqrt{3}\] is
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 =
Find:-
`125^(1/3)`
