Question 1198058

Simplify (32/128)^¾ ÷ (1/64)^-0.5
<pre>{{{((32/128)^(3/4))/(1/64)^(- 0.5)}}}

{{{((1/4)^(3/4))/(1/64)^(- 1/2)}}} ------- Reducing the fractional-base in the numerator and changing - 0.5 to {{{- 1/2}}} in the denominator

{{{((1/4)^(3/4))/matrix(2,1, " ", (64)^(1/2))}}} ----- Appying the law, {{{matrix(1,3, a^(- b), "=", (1/a)^b)}}} in denominator

{{{((2^(- 2))^(3/4))/(2^6)^(1/2))}}} ------ Converting numerator's and denominator's bases to base 2

{{{matrix(2,1, " ", (2^(- 3/2)/(2^3)))}}} ---- Applying {{{matrix(1,3, (a^b)^c, "=", a^(bc))}}}

{{{matrix(1,7, matrix(2,1, " ", 2^(- 3/2 - 3)), "=", 2^(- 3/2 - 6/2), "=", highlight(matrix(2,1, " ", 2^(- 9/2))), or, highlight((1/2)^(9/2)))}}} ----- Applying {{{matrix(1,3, a^b/a^c, "=", a^(b - c))}}}</pre>