Advertisements
Advertisements
Question
Simplify:
`(3/5)^4 (8/5)^-12 (32/5)^6`
Advertisements
Solution
`(3/5)^4 (8/5)^-12 (32/5)^6 = 3^4/5^4 xx (5/2^3)^12 xx (2^5/5)^6` ...`(∵ a^-1 = 1/a)`
= `3^4/5^4 xx 5^12/2^36 xx 2^30/5^6` ...[∵ (am)n = amn]
= `(3^4 xx 5^(12 - 4 - 6))/(2^(36 - 30))` ...`[∵ a^m/a^n = a^(m - n)]`
= `3^4/2^6 xx 5^2`
= `(81 xx 25)/64`
= `2025/64`
APPEARS IN
RELATED QUESTIONS
Simplify the following:
`(2x^-2y^3)^3`
Prove that:
`(a+b+c)/(a^-1b^-1+b^-1c^-1+c^-1a^-1)=abc`
Prove that:
`(a^-1+b^-1)^-1=(ab)/(a+b)`
If abc = 1, show that `1/(1+a+b^-1)+1/(1+b+c^-1)+1/(1+c+a^-1)=1`
Simplify:
`root5((32)^-3)`
Simplify:
`(0.001)^(1/3)`
If `x = a^(m + n), y = a^(n + l)` and `z = a^(l + m),` prove that `x^my^nz^l = x^ny^lz^m`
Write the value of \[\left\{ 5( 8^{1/3} + {27}^{1/3} )^3 \right\}^{1/4} . \]
If \[\sqrt{5^n} = 125\] then `5nsqrt64`=
The simplest rationalising factor of \[2\sqrt{5}-\]\[\sqrt{3}\] is
