Question

Describing an Expression
Which can be used to describe the expression? Check all that apply.

(r -4)3
There are three factors of r -4.
The expression is equal to 1 over 12 factors of r.
Adding the exponents will create an equivalent expression.
Multiplying the exponents will create an equivalent expression.
The expression simplifies to StartFraction 1 Over r Superscript 7 Baseline EndFraction.

Answer 1

Interpret the expression as (r^(-4))^3 = r^(-4·3) = r^(-12) = 1 / r^12.

Which statements are true:
- "There are three factors of r^-4." — True. (It's (r^-4)(r^-4)(r^-4).)
- "The expression is equal to 1 over 12 factors of r." — True (interpreting this as 1 / r^12).
- "Adding the exponents will create an equivalent expression." — False. (For a power of a power you multiply exponents, not add.)
- "Multiplying the exponents will create an equivalent expression." — True. (-4·3 = -12.)
- "The expression simplifies to 1 over r^7." — False. (It simplifies to 1 / r^12.)