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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


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Aug 03, 2011
Equation with Exponents
by: Staff

The question:

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

The answer:

6x¹⁰ = 24x⁶

Solve for x


You 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) = 2


Take the square root of each side of the equation again

√(x*x) = √2

x = ±√2

the final answer is: x = ±√2



check the answer by substituting ±√2 for every x in the original equation (I?m just going to use +√2 for simplicity?s sake)

6x¹⁰ = 24x⁶

6(+√2)¹⁰ = 24(+√2)⁶

6 * (√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 * 8

192 = 192, OK - the answer is correct




This problem can also be solved by adding/subtracting exponents instead of writing out the factors:

6x¹⁰ = 24x⁶

Divide 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 = ±√2



Thanks for writing.

Staff
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