solve and simplify
9^4/3
/
9^2/3
To solve and simplify the expression (9^4/3) / (9^2/3), we can apply the rules of exponents.
Rule 1: When dividing two numbers with the same base, subtract the exponents.
Rule 2: When raising a number to a power, multiply the exponents.
Let's apply these rules step by step:
Step 1: Simplify the numerator:
9^4/3
We can rewrite 9 as 3^2, so the expression becomes:
(3^2)^4/3
According to Rule 2, we multiply the exponents:
3 * 4/3
This simplifies to:
12/3
Step 2: Simplify the denominator:
9^2/3
We can rewrite 9 as 3^2, so the expression becomes:
(3^2)^2/3
Again, according to Rule 2, we multiply the exponents:
2 * 2/3
This simplifies to:
4/3
Step 3: Divide the numerator by the denominator:
(12/3) / (4/3)
According to Rule 1, when dividing with the same base, subtract the exponents:
12/3 - 4/3
This results in:
8/3
Therefore, the simplified expression is 8/3.