Answer:
To simplify the expression 9^4 · 9^(-6), we can use the property of exponents which states that when multiplying exponential expressions with the same base, we can add their exponents.
In this case, we have 9 raised to the power of 4 multiplied by 9 raised to the power of -6.
Using the property mentioned earlier, we can add the exponents together:
9^4 · 9^(-6) = 9^(4 + (-6))
Simplifying the exponent inside the parentheses, we have:
9^(4 + (-6)) = 9^(-2)
Now, we can simplify further by using another property of exponents, which states that when a base is raised to a negative exponent, it can be rewritten as 1 divided by the base raised to the positive exponent.
Applying this property to our expression, we get:
9^(-2) = 1 / 9^2
Finally, we can evaluate 9^2 to get our simplified expression:
1 / 9^2 = 1 / 81
Therefore, the simplified expression of 9^4 · 9^(-6) is 1/81.
Explanation: