Question

Which expressions are equivalent to the one below? Check all that apply. 9^x

Answer 1

Answer:

A) $3^{x}*3^{x}$

B) $3^{2x}$

C) $(3 * 3)^{x}$

Step-by-step explanation:

Given the exponential expression, $9^{x}$:

A)  $3^{x}*3^{x}$ is equivalent to $9^{x}$ due to the Product Rule of exponents:  $a^{m} a^{n} = a^{m + n}$.  

• $3^{x}*3^{x} = 3^{x+x} = 3^{2x}$

Next, apply the Power-to-Power Rule of exponents:  $a^{mn} = (a^{m} )^{n}$.  

• $3^{x}*3^{x} = 3^{x+x} = 3^{2x} = (3^{2})^{x} = 9^{x}$

B)   $3^{2x}$  is equivalent to $9^{x}$ due to the Power-to-Power Rule of exponents:  $a^{mn} = (a^{m} )^{n}$.  

• $3^{2x} = (3^{2})^{x} = (9)^{x} = 9^{x}$.    

C)  $(3 * 3)^{x}$  is equivalent to $9^{x}$ due to the Product-to-Power Rule of exponents:  $(ab)^{m} = a^{m} b^{m}$.  

• $(3 * 3)^{x} = (9)^{x} = 9^{x}$