Determine the values for x & y so that (a) M=1 (b) M>1 (c) 0<M<1 (d) M<0

M= ((16 x^8 y^-4) 1/4) / (32 x^-2 y^8)which simplifies to:M= x^4/(16 y^9)

M= ((16 x^{8} y^{-4})^{ 1/4}) / (32 x^{-2} y^{8})

M = 16^{1/4}(x^{8})^{ 1/4} (y^{-4}) ^{ 1/4} /32 x^{-2}y^{8}

M = 2 x^{2}y^{-1}/32 x^{-2}y^{8}

M = x^{2+2}/(16* y^{8+1})= x^{4}/16y^{9}

^{}

When M >1 , x^{4 }>16y^{9}

When 0< M <1 , 0< x^{4}-16y^{9} < 1

When M >0 y>0 since x^{4 } is always positive

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