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Exponents and Radicals











































The following expression contains both POSITIVE and NEGATIVE EXPONENTS.

x^9•x^4•x^-3

Simplify the expression in two different ways

Comments for Exponents and Radicals

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May 06, 2011
Exponents and Radicals
by: Staff


The question:

x^9•x^4•x^-3


The answer:

I’m going to work this out two different ways:

1) Add the exponents. This is the fastest way to simplify the expression. Since all three of the factors in your expression have the same base (the base is “x”), the exponents can be added directly to arrive at a solution.

2) Factor the entire expression. To understand how these exponents affect the solution, factor the entire expression, and then recombine the factors.

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1) Add the exponents (this is only possible because all three factors have the same base).

x^9•x^4•x^-3

(x^9)•(x^4)•(x^-3)

x^(9+4-3)

x^(10)

x^10

the final answer is: x^10

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2) Factor the entire expression, and then recombine the factors. This will give you a visual picture of the simplification process.


x^9•x^4•x^-3

note:

x^9 = x*x*x*x*x*x*x*x*x

x^4 = x*x*x*x

x^-3 = 1/(x*x*x)


x^9•x^4•x^-3 = (x*x*x*x*x*x*x*x*x*x*x*x*x)/(x*x*x)

three of the x’s in the numerator will cancel three of the x’s in the denominator

(x*x*x*x*x*x*x*x*x*x)*[(x*x*x)/(x*x*x)]

= (x*x*x*x*x*x*x*x*x*x)*1

= x*x*x*x*x*x*x*x*x*x

= x^10

Again, the final answer is: x^10



Thanks for writing.


Staff
www.solving-math-problems.com



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