Algebra 1 Common Core Student Edition, Grade 8-9

How can you check
your answ er?
Su b st i t u t e t h e sa m e
number for the
variable in the original
expression and t he
simplified expression.
The expressions should
be equal.

You can use repeated multiplication to simplify a quotient raised to a power.

XXX X • X • X _ X 3

y'y’y ~y-yy~y3

This suggests another property of exponents.

Pro p ert y Raising a Quotient to a Power

Words To raise a quotient to a power, raise the numerator and the denominator to

the power and simplify.

Algebra I H = w h e r e I a \n a n a i= 0, b + 0, and n is an rational number

Ex a m p l e s ( § M = S ( f ) = ( f f y f

Pro b lem 3 Raisin g a Quotient to a Po w er

/ \3

Multiple Choice What is the simplified form of ( — J?

n n

2 7. 3

15 o ^ 15 125 " 125

z (^33) M Rai se t h e n u m e r a t o r an d t h e d e n o m i n a t o r t o t h e t h i r d p o w er.
5 J 53
zt"3
53
= z i
125
The correct answer is D.
Multiply the exponents in the numerator.
Simplify.
Go t It? 3. a. What is the simplified form of ( j?
b. Reasoning Describe two different ways to simplify the expression
Which method do you prefer? Explain.
You can write an expression of the form ( | j using positive exponents.
(| ) ” = j * Use the definition of negative exponent.
If J
i
Rai se t h e q u o t i e n t t o a p o w er.
3 \4
a 4
a 5
= 1 • hn Multiply by the reciprocal of ^ which is an bn.
un ( u\n
= — = ^ J Simplify. Write the quotient using one exponent.
S°' ( f ) ” = ( I )" f°r aH nonzero numbers a and b and positive integers n.