Simplifying Expressions with Integral Exponents

Simplifying Expressions with Integral Exponents

Recall: Rules of Exponents There are several rules we can follow to help us simplify expressions with integral exponents.

Product Rule

(am)(an) = am+n

23 × 22 = 25

Quotient Rule

am an x5 x3

= am−n = x5−3 = x2

Recall: Rules of Exponents There are several rules we can follow to help us simplify expressions with integral exponents.

Power of a Product

(a×b)n

an×bn

= (4 × 3)2 = 42 × 32 Power of a Power

(am)n = amn (23)2 = 23×2 = 26

Power of a Quotient

a b 3 8

n

( ) ( )

3

an = n b 3 3 = 3 8

Recall: Rules of Exponents There are several rules we can follow to help us simplify expressions with integral exponents.

0 as an Exponent

0 x

= 1

0 5

= 1

Negative Exponent

-n a

1 = n a

Simplified expressions do not include negative exponents.

Recall: Simplifying Exponential Expressions To simplify an exponential expression:

1. Remove all negative exponents.

2. Reduce fractions to simplest terms. 3. Perform all arithmetic.

Application: Joules Simplify the following formula for calculating joules (i.e. the metric unit for energy).

1 J = 1 kg (m × s –1)2

= 1 kg × m2 × s –2 = 1 kg × m2 s2

Power of a Product/Power

Negative Exponent

Simplify the following expression:

6a–1 – (6a)–2

Simplify the following expression:

x(x–1y3)2

Simplify the following expression:

a–1 – b –1 b a – c0 a. b. c.

𝒃 − 𝒂 𝒃 𝒂 𝒃 𝒂𝒄

d. 0 e. cannot be simplified

Simplify the following expression:

a–1 – b –1 b a – c0