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Simplify the expression 9^4·9^−6

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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:

User David Vicente
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