Question 976268
{{{v=(4/3)pi*r^3}}}, and you want to solve for a formula for r.


You must already know about multiplicative inverse.


{{{v(3/4)(1/pi)=r^3}}}


and Symmetric Property of Equality:
{{{r^3=v(3/4)(1/pi)}}}
and you want to know what to do to undo the exponent of 3.


Are you familiar or know some rules or laws about exponents?
Think this way:
{{{r*r*r=r^3}}}

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Starting with r^3, you want the number which must be raised to exponent 3 to give r^3, which is r.
.
{{{root(3,r^3)*root(3,r^3)*root(3,r^3)=(root(3,r^3))^3}}}
which is {{{r^3}}}.
.
More simply {{{root(3,r^3)=r}}}.


Can you conclude the next step or two in the formula, almost finished?



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From here,    {{{r^3=v(3/4)(1/pi)}}}


Take cubed root of both sides.


{{{root(3,r^3)=root(3,v(3/4)(1/pi))}}}


{{{r=root(3,v(3/4)(1/pi))}}}

and with miner simplifying of the rational expression inside the cubed root,
{{{highlight(r=root(3,((3v)/(4pi))))}}}