1) $$ 10^{5} imes 10^{4} $$ 2) $$ a^{3} imes a^{9} $$

Question

1) $$ 10^{5} 	imes 10^{4} $$ 2) $$ a^{3} 	imes a^{9} $$

UpStudy AI · Accepted Answer

Sure, let's simplify each of the expressions using the properties of exponents.

1) **Multiplying Powers with the Same Base:**
   
   $$ 10^{5} \times 10^{4} $$

**Rule:** When multiplying powers with the same base, add the exponents.

$$
   10^{5} \times 10^{4} = 10^{5+4} = 10^{9}
   $$

2) **Multiplying Powers with the Same Base:**
   
   $$ a^{3} \times a^{9} $$

**Rule:** Similarly, when multiplying powers with the same base, add the exponents.

$$
   a^{3} \times a^{9} = a^{3+9} = a^{12}
   $$

**Final Results:**

1. $$ 10^{5} \times 10^{4} = 10^{9} $$

2. $$ a^{3} \times a^{9} = a^{12} $$
$$ 10^{5} \times 10^{4} = 10^{9} $$ and $$ a^{3} \times a^{9} = a^{12} $$.

1) \( 10^{5} \times 10^{4} \) 2) \( a^{3} \times a^{9} \)