Question

Drawing Conclusions
Consider the expression.

6 · 60 · 6–3

Which statements are true about the expression? Check all that apply.
The 6 without an exponent is equivalent to the 6 having a 0 exponent.
The sum of the exponents is 2.
Multiply the exponents to simplify the expression.
The expression has a value of StartFraction 1 Over 36 EndFraction.
An equivalent expression is 65 · 6-7.

Answer 1

Interpret the expression as 6 · 6^0 · 6^(−3).

- True: The expression has value 1/36.
Reason: 6·6^0·6^(−3) = 6^{1+0−3} = 6^{−2} = 1/36.

- True: An equivalent expression is 6^5 · 6^(−7).
Reason: 6^5·6^(−7) = 6^{5−7} = 6^{−2} = 1/36 (same result).

- False: The 6 without an exponent is equivalent to 6^0. (A bare 6 = 6^1, while 6^0 = 1.)
- False: The sum of the exponents is 2. (1 + 0 + (−3) = −2.)
- False: Multiply the exponents to simplify the expression. (When multiplying like bases you add exponents, you do not multiply them.)