Tips For Success

Some questions on tests ask you to simplify an expression. Read the question below. Then follow the tips to answer it.

TIP 1

Use the fact that a fraction a + b c fraction eh plus b , over c end fraction  can be written in the form a c + b c . eh over c , plus , b over c . .

Which expression is equivalent to 20 x 3 y 5 − 30 x 6 y 4 5 x 3 y 3 ? fraction 20 , x cubed , y to the fifth , minus 30 , x to the sixth , y to the fourth , over 5 , x cubed , y cubed end fraction . question mark

1. 4 x 6 y 8 − 6 x 9 y 7 4 , x to the sixth , y to the eighth , minus 6 , x to the ninth , y to the seventh
2. 4 y 2 − 6 x 3 y 4 , y squared , minus 6 , x cubed , y
3. − 2 x 6 y 6 negative 2 , x to the sixth , y to the sixth
4. 15 y 2 − 25 x 3 y 15 , y squared , minus 25 , x cubed , y

TIP 2

When you divide powers that have the same base, you subtract the exponents.

Think It Through

Write the expression as a difference of two fractions. Then simplify each fraction using the laws of exponents.

20 x 3 y 5 − 30 x 6 y 4 5 x 3 y 3 = 20 x 3 y 5 5 x 3 y 5 − 30 x 6 y 4 5 x 3 y 3 = 4 x 3 − 3 y 5 − 3 − 6 x 6 − 3 y 4 − 3 = 4 x 0 y 2 − 6 x 2 y 1 = 4 y 2 − 6 x 3 y table with 5 rows and 1 column , row1 column 1 , fraction 20 , x cubed , y to the fifth , minus 30 , x to the sixth , y to the fourth , over 5 , x cubed , y cubed end fraction , row2 column 1 , equals . fraction 20 , x cubed , y to the fifth , over 5 , x cubed , y to the fifth end fraction . minus . fraction 30 , x to the sixth , y to the fourth , over 5 , x cubed , y cubed end fraction , row3 column 1 , equals 4 . x super 3 minus 3 end super . y super 5 minus 3 end super . minus 6 . x super 6 minus 3 end super . y super 4 minus 3 end super , row4 column 1 , equals 4 , x to the , y squared , minus 6 , x squared , y to the first , row5 column 1 , equals 4 , y squared , minus 6 , x cubed , y , end table