Easy Algebra Step-by-Step

78 Easy Algebra Step-by-Step

Problem Simplify.

a. ()^23 )

b. ()y^35 )

Solution

a.()^23 )

Step 1. Keep the same base x and multiply the

exponents 2 and 3.

()^23 )) xx^23 =x^6

b. ()y^35 )

Step 1. Keep the same base y and multiply the exponents 3 and 5.

()yy^35 )) y^35 =y^15

Rule for the Power of a Product

()ypp=xyx p

This rule tells you that a product raised to

a power is the product of each factor raised to

the power.

Problem Simplify.

a. ()y^6

b. ()^3

c. ()^32 y^4

Solution

a.()y^6

Step 1. Raise each factor to the power of 6.

()y^66 =xy^6

b. ()^3

Step 1. Raise each factor to the power of 3.

() 44 )))^33444 xx^33 = 6464 x

P

(^23) ))) ≠x (^5). For a power to a power,
multiply exponents, don’t add.
Confusing the rule ()ypp=xyx p
with the rule xxmnx =xmn+ is a
common error. Notice that the rule
()ypp=xyx p has the same exponent
and different bases, while the rule
xxmnx =xmn+ has the same base and
different exponents.