Order the expression by choosing >, <, or = .
2^3 × 2^2 _ 2^6
2^2 × 3^2 _ 6^3
2^3 × 3^2 _ 6^2
http://www.regentsprep.org/regents/math/algebra/ao5/rule_pmu.htm
I'll be glad to check your answers.
To order each expression, we can simplify them by evaluating the exponentiation first and then comparing the results.
For the first expression, we have:
2^3 × 2^2 _ 2^6
Expanding each term, we get:
8 × 4 _ 64
Evaluating each term, we have:
32 _ 64
Since 32 is less than 64, we can write:
32 < 64
For the second expression, we have:
2^2 × 3^2 _ 6^3
Expanding each term, we get:
4 × 9 _ 216
Evaluating each term, we have:
36 _ 216
Since 36 is less than 216, we can write:
36 < 216
For the third expression, we have:
2^3 × 3^2 _ 6^2
Expanding each term, we get:
8 × 9 _ 36
Evaluating each term, we have:
72 _ 36
Since 72 is greater than 36, we can write:
72 > 36
To summarize the order of the expressions:
32 < 64
36 < 216
72 > 36