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# Stuck on a rational exponent question.

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Please help! I would like someone to explain and walk me step by step on how to solve this question. I know what to do in the beginning, but I am kinda stuck on what to do next. Do we have to multiply the exponents? Thanks!

"The length, L, of the longest board that can be carried horizontally around the right-angle corner of the two intersecting hallways is L = (a^2/3 + b^2/3)^3/2, where a and b represent the width, in centimetres, of the hallway. What is the longest piece of plywood a carpenter can carry horizontally around the corner of the two intersecting hallways if one hallway is 150 cm wide and the other is 200 cm wide? Round to the nearest hundredth."

Apr 18, 2019

#1
+81
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Yes, you would multiply the exponents due to the exponent rule of (xa)b = xa*b.

$$(a^\frac{2}{3}+b^\frac{2}{3})^\frac{3}{2} = a^{\frac{2}{3}*\frac{3}{2}}+b^{\frac{2}{3}*\frac{3}{2}}$$

The 2/3 and 3/2 cancel out to one in both cases, so L is just equal to a+b.

In this case, a+b = 150+200, which is 350 cm wide.

Apr 18, 2019
#3
+7499
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Please notice that $$(a+b)^n \neq a^n+b^n$$.

MaxWong  Apr 18, 2019
#2
+18360
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L = [ (150^(2/3) + 200^(2/3) ] ^(3/2)    = (28.231  + 34.1996)^(3/2) =   62.43^(3/2) = 493.28 cm

Apr 18, 2019