How do you simplify $(2x^(-7/4))/(4x^(4/3))$ ?

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Answer 1 · 2016-12-19T14:42:12

$1/(2x^(37/12))$

We can modify this expression to:

$(2*x^(-7/4))/(2*2*x^(4/3)$

$(color(red)(cancel(color(black)(2)))*x^(-7/4))/(color(red)(cancel(color(black)(2)))*2*x^(4/3)$

$x^(-7/4)/(2x^(4/3))$

We can now use the rule for exponents which states:

$color(red)(x^a/x^b = 1/x^(b - a))$

$1/(2x^(4/3 - -7/4))$

$1/(2x^(4/3 + 7/4))$

$1/(2x^(16/12 + 21/12))$

$1/(2x^(37/12))$

How do you simplify (2x^(-7/4))/(4x^(4/3))(2x^(-7/4))/(4x^(4/3))?