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Law of Exponent

by Sharina
(Philippines)











































Simplify the following expression.

8x9/2x5=

Options:

1. Factor both both the numerator and denominator. The common factors can be canceled.

2. Simplify the expression by subtracting the exponents.

Comments for Law of Exponent

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Oct 14, 2011
Reducing Fractions with Exponents
by: Staff


Question:

by Sharina
(Philippines)

8x9/2x5=


Answer:

8x⁹ / 2x⁵ =


This fraction can be simplified by subtracting the exponents:

8x⁹ / 2x⁵

= 2³x⁹ / 2¹x⁵

= 2⁽³⁻¹⁾x⁽⁹⁻⁵⁾

= 2⁽²⁾x⁽⁴⁾

= 2²x⁴

= 4x⁴


However, to understand the process, it’s probably helpful to factor both the numerator and denominator. The common factors can be canceled:

8 = 2 * 2 * 2

x⁹ = x * x * x * x * x * x * x * x * x

2 = 1 * 2

x⁵ = x * x * x * x * x

2 * 2 * 2 *x⁹ / 2x⁵ =

8 = 2 * 2 * 2


8x⁹ / 2x⁵

= [(2 * 2 * 2) * (x * x * x * x * x * x * x * x * x)] / [(2) * (x * x * x * x * x)]


Factors which appear in the numerator AND denominator can be canceled:

= [(2 * 2) * (x * x * x * x)] * (2 / 2) * (x / x) * (x / x) * (x / x) * (x / x) * (x / x)

= [(2 * 2) * (x * x * x * x)] * (1) * (1) * (1) * (1) * (1) * (1)

= [(2 * 2) * (x * x * x * x)]

= (2²) * (x⁴)

= 4 * x⁴

= 4x⁴

The final answer is: 4x⁴



Thanks for writing.

Staff
www.solving-math-problems.com



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