How do you evaluate #w^ { \frac { 1} { 4} } \div w ^ { \frac { 5} { 4} }#?

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Answer 1 · 2017-12-06T02:51:10

See a solution process below:

First, rewrite the expression as:

#w^(1/4)/w^(5/4)#

Next, use this rule of exponents to combine the numerator and denominator:

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

#w^color(red)(1/4)/w^color(blue)(5/4) = 1/w^(color(blue)(5/4)-color(red)(1/4)) = 1/w^(4/4) = 1/w^1#

Now, use this rule of exponents to complete the evaluation:

#a^color(red)(1) = a#

#1/w^color(red)(1) = 1/w#