Question

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). The exponents are 1, 0, and −3 (the lone 6 = 6^1).

True:
- The expression has a value of 1/36. Reason: 6^1·6^0·6^(−3) = 6^(1+0−3) = 6^(−2) = 1/36.
- An equivalent expression is 6^5 · 6^(−7). Reason: 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. (6 without an exponent is 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, not multiply them.)