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

True:
- The expression has a value of 1/36. (6 · 6^0 · 6^−3 = 6^(1+0−3) = 6^(−2) = 1/6^2 = 1/36.)
- An equivalent expression is 6^5 · 6^(−7) (because 6^5·6^(−7) = 6^(5−7) = 6^(−2) = 1/36).

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