Question

Compare. Use <, >, or = to complete the statement. (2^7)^2 2^10 * 2^2

Answer 1

(2^7)^2 __ (2^10) * (2^2)
2^(7 * 2) __ 2^(10 + 2)
2^14 __ 2^12

2^14 > 2^12

Answer 2

(2^7)^2 > 2^10 * 2^2

Explanation:

Use <, >, or = to complete the statement.

(2^7)^2------ 2^10 * 2^2

To compare we simplify the left side and right side as well

Apply exponential property

(a^m)^n = a^mn

`(2^7)^2 = 2^(14)`

a^m * a^n = a^m+n

`2^(10) * 2^2= 2^(12)`

2^14 ------- 2^12

Now we compare the exponents

14 is greater than 12

so (2^7)^2 > 2^10 * 2^2