Question

Which expressions are equivalent to the one below? Check all that apply.

Answer 1

Answer: C. $7^x * 7^x$

D. $(7* 7)^x$

F. $7^{2x}$

Step-by-step explanation:

Law of exponents :

$a^m*a^n=a^{m+n}\\(a^m)^n=a^{mn}$

$49^x=(7^2)^x=7^{2x}$

A. $7*7^x$

$=7^{1+x}\neq49^x$

B. $7 * 7^2x$

=$7^{1+2x}\neq49^x$

C. $7^x * 7^x$

$=7^{x+x}=7^{2x}=(7^2)^x=49^x$

D. $(7* 7)^x$

$=(7^2)^x=49^x$

E. $7^2* 7^x$

$7^{2+x}\neq49^x$

F. $7^{2x}=(7^2)^x=49^x$

Answer 2

The answers are C, D, and F.

The result is 49ˣ

Let's check all choices:
A. 7 * 7ˣ = 7¹ * 7ˣ = 7¹⁺ˣ
B. 7 * 7²ˣ = 7¹ * 7³ˣ = 7¹⁺²ˣ
C. 7ˣ * 7ˣ = 7ˣ⁺ˣ = 7²ˣ = (7²)ˣ = 49ˣ - CORRECT
D. (7 * 7)ˣ = 49ˣ - CORRECT
E. 7² * 7ˣ = 7²⁺ˣ
F. 7²ˣ = (7²)ˣ = 49ˣ - CORRECT