MEDALSif you help me! help please:) simplify the following expressions:
1. (4p^1/4q^-3)^1/2
2. (5b)^-1/(8b^6)^1/3
3. (2x^6y^8)^1/4 x (8x^-2)^1/4
4. (m^1/3n^1/2)^2 x (m^1/6n^1/3)^4 x (mn)^-2

Question

anonymous · Answer

1)$$(\frac{ 4p }{ 4q^{-3} })^{1/2} = \frac{ p^{1/2} }{ q^{-3/2} } = p^{1/2}q^{3/2}$$

anonymous · Answer

2) $$\frac{ (5b)^{-1} }{ (8b^{6})^{1/3} }= \frac{ 1 }{ 5b * 8^{1/3}*b^{6/3} } = \frac{ 1 }{ 5b * 2*b^{2} }$$

anonymous · Answer

thanks @xon1300

anonymous · Answer

3)
$$(2x ^{6}y^{8})^{1/4} * (8x^{-2})^{1/4} = 2^{1/4}*x^{6/4}*y^{8/4}*8^{1/4}*x^{-2/4}$$
$$= 2 *x * y ^{2}$$

anonymous · Answer

wait , the answers to number 1 is 2p^1/8 q^1/3 (have the answersin the back of my text book) just need the working though
and the answer to number 2 is 1/10 b^-3

anonymous · Answer

number 3 is correct though, thanks

anonymous · Answer

$$(m^{1/3}n^{1/2})^{2} * (m^{1/6}n^{1/3})^{4} * (mn)^{-2} = (m^{2/3}n) * (m^{2/3}n^{4/3}) * m^{-2}n^{-2} $$
$$=m^{4/3} n^{7/3} * m^{-2}n^{-2} $$
$$=m^{-2/3} * n^{1/3}$$