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# 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?

1 answers

Fotios TsitsosI love using Mathematics and Science to explain and understand the world.17.5k students helped

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.