S.I.M.
S.I.M.

STRATEGIC INTERVENTION MATERIAL

By: gene Adrian p. curioso ii-neuron Zero and negative exponents
Zero and negative exponents

The laws of exponent can also be extended to include zero and negative integers.
Consider two ways of simplifying the expression 2 32 3 2 32 3=2∙2∙22∙2∙2=1 2 32 3=23-3==20
Therefore, 20=1 since 2 32 3 cannot have two different values.
Remember
For any nonzero number a, a0=1 Illustrative Examples: A. 50=1 B. 8x2y0=8∙x2∙1=8x2 C. 4x2y3z 0

Now, consider two ways of simplifying the expression 2327 2327=2∙2∙22∙2∙2∙2∙2∙2∙2 2327=23-7 =12⋅2⋅2⋅2=124 =2-4
Therefore, 2-4=124 since 2327 cannot have two different value.
Remember
In general, for any nonzero number a and any integer n a-n=1an Examples: A. a-5=1a-5 B. 3x -3=13x 3=127x3 C. 14x2y -2=4x2y 2=16x4y2

Evaluating expressions with zero and negative exponents
The laws of exponents for division can be summarized, such that aman=am-n ;m>n, a≠0 aman=a0or 1;m=n, a≠0 aman=1am-n;m <n, a ≠0
Since the first law for division has been discussed, concentrate on expressions with zero and negative exponents. Skill can be achieved by consistent practice.

Rewriting algebraic expressions with zero
And negative exponents
When algebraic expressions have zero and negative exponents, they have to be rewritten in a way that all exponents must be positive. In all cases, it is assumed that all denominators are not equal to zero.
Examples:
A. Simplify: 3x3y 512x5y 5
Solution: 3x3y 512x5y 5=312x3x5y5y5 =14x-2y 0=141x21=14x2 B. Simplify: 144s3t -49r-2s5t-2
Solution: 144s3t -49r-2s5t-2=14491r-2s3s5t-4t-2 =16r2s-2t-2=16r2s2t2

Simplifying exponential expressions
Exponential expressions are said to be in simplest form if: 1. All the exponents are positive, 2. There are no powers of powers, 3. Each base appears only once, and 4. All fractions are in simplest form.

Examples: A. Simplify : 5a2b3 010a3b2 -1, a≠0,b≠0
Solution : 5a2b3 010a3b2 -1=1110a3b2=1⋅10a3b2=10a3b2 B. Simplify : 3x -2(x3) -1
Solution : 3x -2(x3) -1=3-2⋅x-21x3=132⋅1x2⋅x31=x39x2=x3-29=x9

C. Simplify : 3x2y0(18x-3y) -1

Solution : 3x2y018x-3y -1=3x2⋅1⋅118x-3y =318⋅x2⋅x3⋅1y=3x518y=x56y D. Simplify : 212⋅31527⋅612
Solution : 212⋅31527⋅612=212⋅31533(2⋅3) 12 =212⋅31533⋅212⋅312 =212212⋅31533⋅312 1⋅1=1

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