We found that (-3)^(-8) is equal to 16561. Next, let's evaluate the second expression -3^8. We will use the Negative Exponent Property again. -3^(-8)=-1/3^8 To simplify this we can once again use the Power of Products Property.

-1/3^8

SplitIntoFactors

Split into factors

-1/3^(2*4)

ProdInExponent

a^(m* n)=(a^m)^n

-1/(3^2)^4

▼

Simplify

CalcPow

Calculate power

-1/(9)^4

Rewrite

Rewrite (9)^4 as 9*9*9*9

-1/9*9*9*9

Multiply

-1/6561

We evaluated both expressions. Let's summarize our results.

Expression	Evaluation
(-3)^(-8)	1/6561
-3^(-8)	-1/6561

This time we will evaluate the following expressions. (-3)^(-9) and-3^(-9) Like in the previous part, we will use the Negative Exponent Property.

Negative Exponent Property
If a is a non-zero real number, then the following equation is true. a^(- n)=1/a^n

First, let's use this property to evaluate (-3)^(-9). (-3)^(-9)=1/(-3)^9 To simplify this, we can use the Power of Products Property.

1/(-3)^9

SplitIntoFactors

Split into factors

1/(-3)^(3*3)

ProdInExponent

a^(m* n)=(a^m)^n

1/((-3)^3)^3

a^3=a* a* a

1/((-3)(-3)(-3))^3

Multiply

1/(-27)^3

a^3=a* a* a

1/(-27)(-27)(-27)

Multiply

1/-19 683

MoveNegDenomToFrac

Put minus sign in front of fraction

-1/19 683

We found that (-3)^(-9) is equal to - 119 683. Next let's evaluate the second expression, -3^9. We will use the Negative Exponent Property again. -3^(-9)=-1/3^9 To simplify this we can once again use the Power of Products Property.

-1/3^9

SplitIntoFactors

Split into factors

-1/3^(3*3)

ProdInExponent

a^(m* n)=(a^m)^n

-1/(3^3)^3

▼

Simplify

a^3=a* a* a

-1/(3*3*3)^3

Multiply