How do you write #7^(3/4)# in radical form?

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Answer 1 · 2016-10-15T01:24:19

#(root(4)7)^3# or #root(4)(7^3#

#7^(3/4)#

The numerator of the rational exponent represents the "power".
The denominator represents the "root".

A trick to remembering this is the saying "higher power" for the numerator and "the roots of a plant are at the bottom" for the denominator.

In this example #7^(color(red)3/4)#, the numerator #color(red)3# is the "power" or exponent of the final expression.

The denominator #color(blue)4# in #7^(3/color(blue)4# is the root.

#(root(color(blue)4)7)^color(red)3#

This can also be written as #root(color(blue)4)(7^color(red)3)#