Advertisements
Advertisements
प्रश्न
Prove that:
`(3^-3xx6^2xxsqrt98)/(5^2xxroot3(1/25)xx(15)^(-4/3)xx3^(1/3))=28sqrt2`
उत्तर
We have to prove that `(3^-3xx6^2xxsqrt98)/(5^2xxroot3(1/25)xx(15)^(-4/3)xx3^(1/3))=28sqrt2`
Let x = `(3^-3xx6^2xxsqrt98)/(5^2xxroot3(1/25)xx(15)^(-4/3)xx3^(1/3))`
`=(3^-3xx3^2xx2^2xxsqrt(7xx7xx2))/(5^2xxroot3(1/25)xx(15)^-(4/3)xx3^(1/3))`
`=(3^(-3+2)xx2^2xx7sqrt2)/(5^2xx1/5^(2xx1/3)xx5^(-4/3)xx3^(-4/3)xx3^(1/3))`
`=(3^-1xx2^2xx7sqrt2)/(5^2/1xx1/5^(2/3)xx1/5^(4/3)xx1/3^(4/3)xx3^(1/3)/1)`
`=3^-1xx2^2xx7sqrt2xx1/5^2xx5^(2/3)xx5^(4/3)xx3^(4/3)xx1/3^(1/3)`
`=3^-1xx3^(4/3)xx1/3^(1/3)xx4xx7sqrt2xx1/5^2xx5^(2/3)xx5^(4/3)`
`=3^(-1+4/3-1/3)xx4xx7sqrt2xx5^(-2+2/3+4/3)`
`=3^((-1xx3)/(1xx3)+4/3-1/3)xx28sqrt2xx5^((-2xx3)/(1xx3)+2/3+4/3)`
`=3^((-3+4-1)/3)xx28sqrt2xx5^((-6+2+4)/3)`
`=3^0xx28sqrt2xx5^0`
`=1xx28sqrt2xx1`
`=28sqrt2`
Hence, `(3^-3xx6^2xxsqrt98)/(5^2xxroot3(1/25)xx(15)^(-4/3)xx3^(1/3))=28sqrt2`
APPEARS IN
संबंधित प्रश्न
Find:-
`9^(3/2)`
Solve the following equation for x:
`7^(2x+3)=1`
Solve the following equation for x:
`2^(x+1)=4^(x-3)`
Find the value of x in the following:
`2^(x-7)xx5^(x-4)=1250`
Solve the following equation:
`3^(x+1)=27xx3^4`
If a and b are distinct primes such that `root3 (a^6b^-4)=a^xb^(2y),` find x and y.
Write the value of \[\left\{ 5( 8^{1/3} + {27}^{1/3} )^3 \right\}^{1/4} . \]
If a, b, c are positive real numbers, then \[\sqrt[5]{3125 a^{10} b^5 c^{10}}\] is equal to
If (16)2x+3 =(64)x+3, then 42x-2 =
\[\frac{5^{n + 2} - 6 \times 5^{n + 1}}{13 \times 5^n - 2 \times 5^{n + 1}}\] is equal to
