Advertisements
Advertisements
प्रश्न
Simplify:
`(9^(1/3) xx 27^(-1/2))/(3^(1/6) xx 3^(- 2/3))`
उत्तर
`(9^(1/3) xx 27^(-1/2))/(3^(1/6) xx 3^(-2/3)) = ((3^2)^(1/3) xx (3^3)^(-1/2))/(3^(1/6) xx 3^(-2/3))` ...[∵ (am)n = amn]
= `(3^(2/3) xx 3^(-3/2))/(3^(1/6) xx 3^(-2/3))` ...[∵ am × an = am + n]
= `(3^(2/3 - 3/2))/(3^(1/6 - 2/3))`
= `(3^((4 - 9)/6))/(3^((1 - 4)/6))` ...`[∵ a^m/a^n = a^(m - n)]`
= `(3^(-5/6))/(3^(-3/6)`
= `3^(- 5/6 + 3/6)`
= `3^(-2/6)`
= `3^(-1/3)`
APPEARS IN
संबंधित प्रश्न
Simplify the following:
`(5^(n+3)-6xx5^(n+1))/(9xx5^x-2^2xx5^n)`
Solve the following equation for x:
`2^(5x+3)=8^(x+3)`
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrtx)^((-2)/3)sqrt(y^4)divsqrt(xy^((-1)/2))`
Assuming that x, y, z are positive real numbers, simplify the following:
`root5(243x^10y^5z^10)`
Show that:
`{(x^(a-a^-1))^(1/(a-1))}^(a/(a+1))=x`
Solve the following equation:
`sqrt(a/b)=(b/a)^(1-2x),` where a and b are distinct primes.
If a and b are different positive primes such that
`(a+b)^-1(a^-1+b^-1)=a^xb^y,` find x + y + 2.
Write \[\left( \frac{1}{9} \right)^{- 1/2} \times (64 )^{- 1/3}\] as a rational number.
If (x − 1)3 = 8, What is the value of (x + 1)2 ?
If \[8^{x + 1}\] = 64 , what is the value of \[3^{2x + 1}\] ?
