Answer:
The simplest form of the expression is 3² ⇒ 3rd answer
Step-by-step explanation:
- The expression is 3 power 3 multiplied by 3 power 3 over 3 power 4
∵ 3 power 3 = 3³
∵ multiplied by 3 power 3 = × 3³
∵ over 3 power 4 = ÷ [tex]3^{4}[/tex]
- Lets write all of them in one expression
∴ The expression = [tex]\frac{3^{3}*3^{3}}{3^{4}}[/tex]
- All the numbers in the expression is 3 to the power
∴ The expression have the same base 3
- Remember: if we have numbers of same base multiplied then we
add their powers and if divided then we subtract their powers
[tex]\frac{a^{m}*a^{n}}{a^{q}}=a^{m+n-q}[/tex]
- Lets use this rule to simplify the expression
∵ The expression = [tex]\frac{3^{3}*3^{3}}{3^{4}}[/tex]
- Use the rule of the same base above
∴ [tex]\frac{3^{3}*3^{3}}{3^{4}}[/tex] = [tex]3^{3+3-4}=3^{6-4}=3^{2}[/tex]
∴ The simplest form of the expression is 3²
