Beginning and Intermediate Algebra - Wallace Math Courses ...

x 4
2 y 4
6 · 2x 1
2 y 5
6
x 7
2y0 2x 5
2 y 9
6
x 7
2
Example 416.
⎛
⎝
⎛
⎝ 25x1 3 y 2
5
9x 4
5 y −3
2
25x 5
15 y 4
10
9x 12 15
−
15 y 10
Add exponents in numerator, in denominator, y 0 =1
Subtract exponents onx, reduce exponent on y
2x −1 y 3
2 Negative exponent moves down to denominator
2y 3
2
x
⎞
⎠
⎞
⎠
− 1
2
− 1
� 7
−
25x 15 y 19 � 1
−
2
10
9
�
9
7
−
25x 15 y 19
10
9 1
2
Our Solution
Using order of operations, simplify inside parenthesis first
Need common denominators before we can subtract exponents
2 Subtract exponents, be careful of the negative:
4
10 −
�
− 15
�
=
10
4 15 19
+ =
10 10 10
�1
2
25 1 7
−
2 x 30 y 19
20
3x 7
30
5y 19
20
The negative exponent will flip the fraction
The exponent 1
goes on each factor
2
Evaluate 9 1
2 and 25 1
2 and move negative exponent
Our Solution
It is important to remember that as we simplify with rational exponents we are
using the exact same properties we used when simplifying integer exponents. The
only difference is we need to follow our rules for fractions as well. It may be worth
reviewing your notes on exponent properties to be sure your comfortable with
using the properties.
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