# Algebra - Equation with Exponents

when dividing the equation 6x^10+24x^6

3X^2 i divided it to its simple form now equallying 2x^10=8x^6 with the denomatior being x^2 im not sure where to go.. if the x^2 id subtracted from both the exponents or only one.. i need help please

### Comments for Algebra - Equation with Exponents

 Aug 03, 2011 Equation with Exponents by: Staff The question:when dividing the equation 6x^10+24x^63X^2 i divided it to its simple form now equallying 2x^10=8x^6 with the denomatior being x^2 im not sure where to go.. if the x^2 id subtracted from both the exponents or only one.. i need help pleaseThe answer: 6x¹⁰ = 24x⁶Solve for xYou began the problem by dividing each side of the equation by 3x²(6x¹⁰)/(3x²) = (24x⁶)/(3x²)Although it is not necessary, I am going to write down all the factors so you can see the entire process in detail:(2*3*x*x*x*x*x*x*x*x*x*x)/(3*x*x) = (2*2*2*3*x*x*x*x*x*x)/(3*x*x)Cancel common factors which appear in both the numerator and denominator(2*x*x*x*x*x*x*x*x*)*(3/3)*[(x*x)/(x*x)] = (2*2*2*x*x*x*x)*(3/3)*[(x*x)/(x*x)](2*x*x*x*x*x*x*x*x*)*(1)*(1) = (2*2*2*x*x*x*x)*(1)*(1)(2*x*x*x*x*x*x*x*x*) = (2*2*2*x*x*x*x)Divide each side of the equation by 2x⁴(2*x*x*x*x*x*x*x*x*)/2x⁴ = (2*2*2*x*x*x*x)/2x⁴(2*x*x*x*x*x*x*x*x*)/(2*x*x*x*x) = (2*2*2*x*x*x*x)/(2*x*x*x*x)Cancel common factors which appear in both the numerator and denominator(x*x*x*x)*(2/2)*[(x*x*x*x)/( x*x*x*x)] = (2*2)*(2/2)*[(x*x*x*x)/( x*x*x*x)] (x*x*x*x)*(1)*(1)= (2*2)*(1)*(1)(x*x*x*x) = (2*2)Take the square root of each side of the equation (we could take the 4th root and complete the problem in 1 step, but I am going to take the square root twice)√(x*x*x*x) = √(2*2)(x*x) = 2Take the square root of each side of the equation again√(x*x) = √2x = ±√2the final answer is: x = ±√2check the answer by substituting ±√2 for every x in the original equation (I?m just going to use +√2 for simplicity?s sake)6x¹⁰ = 24x⁶6(+√2)¹⁰ = 24(+√2)⁶6 * (√2 * √2 * √2 * √2 * √2 * √2 * √2 * √2 * √2 * √2 ) = 24 * (√2 * √2 * √2 * √2 * √2 * √2)6 * (2 * 2 * 2 * 2 * 2) = 24 * (2 * 2 * 2)6 * 32 = 24 * 8192 = 192, OK - the answer is correctThis problem can also be solved by adding/subtracting exponents instead of writing out the factors:6x¹⁰ = 24x⁶Divide each side of the equation by 6x⁶(6x¹⁰)/(6x⁶) = 24x⁶/(6x⁶)1*(x¹⁰⁻⁶) = 4*(x⁶⁻⁶)(x⁴) = 4*(x⁰)x⁴ = 4*(1)x⁴ = 4∜(x⁴) = ∜4 x = ±√2Thanks for writing.Staff www.solving-math-problems.com

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