   SEARCH HOME Math Central Quandaries & Queries  Question from niiaryee, a student: (((((5^2*4^3)1/5+9^3/3)+(25+(4*5)/15)^2-10)/10/2)3))))) Hi Niiaryee,

Look at the innermost nested parentheses, evaluate that and work your way out of the mess of parentheses. Starting on the left and looking for the innermost nested parentheses I see

$((((\;{ \bf (5^2 * 4^3)}\; 1/5+9^3/3)+(25+(4*5)/15)^2-10)/10/2)3))))).$

$5^2 * 4^3 = 25 * 64 = 1600$ so what you have now is $1600 * \frac15 = 320$ so you problem reduces to

$(((( 320 +9^3/3)+(25+(4*5)/15)^2-10)/10/2)3)))))$

and one set of parentheses is gone.

Starting on the left and looking again for the innermost nested parentheses I see

$(((\; { \bf( 320 +9^3/3)}\; +(25+(4*5)/15)^2-10)/10/2)3))))).$

$9^3 = 9 \times 9 \times 9 = 729.$ Division takes precedence over addition and $\frac{729}{3} = 243,$ hence you have

$(((563+(25+(4*5)/15)^2-10)/10/2)3)))))$

and you have removed one more set of parentheses.

The next set of innermost parentheses I see is

$(((563+(25+\; {\bf (4*5)}\; /15)^2-10)/10/2)3)))))$

and you can complete the problem from here,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.