Asked by LaurenMaths 💯

How do I find n? There is a rectangle and l=125^2n and w=25^n-1 and there area in 625cm^2. I know n=3/4 and I know you have to multiply l and w. What steps are required after that?

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Fotios Tsitsos

I love using Mathematics and Science to explain and understand the world.

The formula for the area is l•w so your data gives you the exponential equation: 125^(2n) • 25^(n-1) = 625. Notice now that every term in the equation has a base that is a power of 5: 5^2= 25, 5^3=125 and 5^4=625. Using power rules, you can write your equation as: 5^(3•2n) • 5^(2•(n-1))=5^4 or more simply: 5^(6n+2n-2)=5^4 In the equation, since the bases of both sides are the same, it means that the exponents should be equal. Therefore you get: 8n-2=4, or 8n=6 so n=6/8 or 3/4.

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