Question

17. Evaluate each pair of expressions.
a. (-3)-8 and -3-8
b. (-3)-9 and -3-9

Answer 1

Both pairs of expressions, (-3)-8 and -3-8, as well as (-3)-9 and -3-9, yield the same results, -11 and -12 respectively since subtraction with negative numbers follows consistent rules.

Step-by-step explanation:

The question requires evaluating two pairs of expressions involving negative numbers. In mathematics, the way negative signs are handled can change the result of an expression.

For the first pair of expressions:

• (-3)-8 is equivalent to -3 - 8, which equals -11.
• -3-8 is just another way of writing the same expression, so it also equals -11.

Both expressions in part

a

yield the same result since the subtraction of a positive number is similarly executed, regardless of parentheses.

For the second pair of expressions:

• (-3)-9 is equivalent to -3 - 9, which equals -12.
• -3-9 again is simply a different notation for the same expression, so it also equals -12.

Similarly, both expressions in part

b

will result in the same outcome for the same reason expressed above.

Answer 2

Each should be evaluated as follows;

a.
`(-3)^(-8)=(1)/(6561)` and
`-3^(-8)=-(1)/(6561)`

b.
`(-3)^(-9)=-(1)/(19683)` and
`-3^(-9)=-(1)/(19683)`

In Mathematics and Euclidean Geometry, an exponent can be represented or modeled by this mathematical expression;

`b^n`

Where:

• b represents the base.
• the variables b and n are numbers (numerical values), letters, or an algebraic expression.
• n is known as a superscript or power.

Part a.

Based on the information provided, we can logically deduce the following;

`(-3)^(-8)=(1)/((-3)^(8)) \\\\(-3)^(-8)=(1)/(6561)\\\\\\\\-3^(-8)=-(1)/(3^(8)) \\\\-3^(-8)=-(1)/(6561)`

Part b.

Based on the information provided, we can logically deduce the following;

`(-3)^(-9)=(1)/((-3)^(9)) \\\\(-3)^(-9)=-(1)/(19683)\\\\\\\\-3^(-9)=-(1)/(3^(9)) \\\\-3^(-9)=-(1)/(19683)`

Complete Question:

Evaluate each pair of expressions.

a.
`(-3)^(-8)` and
`-3^(-8)`

b.
`(-3)^(-9)` and
`-3^(-9)`