Question

Put the expressions in order from least to greatest.
A.) 11^4/11^11
B.) 1/11^-4
C.) (11^-3)^-3
D.) 11^5 x 11^2

Answer 1

To compare the expressions, we can simplify each one.

A.) \( 11^4 / 11^{11} = 11^{4 - 11} = 11^{-7} \)

B.) \( 1 / 11^{-4} = 11^4 \)

C.) \( (11^{-3})^{-3} = 11^{-3 \times -3} = 11^{9} \)

D.) \( 11^5 \times 11^2 = 11^{5 + 2} = 11^{7} \)

Now we have:

- A: \( 11^{-7} \)
- B: \( 11^4 \)
- C: \( 11^9 \)
- D: \( 11^7 \)

To order them from least to greatest, we look at the exponents:

1. \( 11^{-7} \) (smallest exponent)
2. \( 11^4 \) (next)
3. \( 11^7 \)
4. \( 11^9 \) (largest exponent)

Thus, the order from least to greatest is:

**A, B, D, C**.