Advertisements
Advertisements
Question
Simplify:
`((5^-1xx7^2)/(5^2xx7^-4))^(7/2)xx((5^-2xx7^3)/(5^3xx7^-5))^(-5/2)`
Advertisements
Solution
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
RELATED QUESTIONS
Prove that:
`1/(1 + x^(b - a) + x^(c - a)) + 1/(1 + x^(a - b) + x^(c - b)) + 1/(1 + x^(b - c) + x^(a - c)) = 1`
Solve the following equations for x:
`2^(2x)-2^(x+3)+2^4=0`
Prove that:
`sqrt(1/4)+(0.01)^(-1/2)-(27)^(2/3)=3/2`
Find the value of x in the following:
`5^(2x+3)=1`
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.
The value of \[\left\{ 8^{- 4/3} \div 2^{- 2} \right\}^{1/2}\] is
If \[\frac{2^{m + n}}{2^{n - m}} = 16\], \[\frac{3^p}{3^n} = 81\] and \[a = 2^{1/10}\],than \[\frac{a^{2m + n - p}}{( a^{m - 2n + 2p} )^{- 1}} =\]
If x = \[\frac{2}{3 + \sqrt{7}}\],then (x−3)2 =
The value of \[\sqrt{5 + 2\sqrt{6}}\] is
Simplify:
`(3/5)^4 (8/5)^-12 (32/5)^6`
