Answer:
To multiply two numbers with exponents, you add the exponents. In this case, you want to multiply (9^(-3)) by (9^(12)).
Using the rule of adding exponents, we can rewrite the expression as (9^(-3 + 12)).
Now, let's simplify the exponent: (-3 + 12) = 9.
So, the expression becomes (9^9).
Therefore, (9^(-3))(9^(12)) is equal to 9 raised to the power of 9, which can be written as 9^9.
Explanation:
Certainly! Let's break down the expression step by step:
The expression is (9^(-3))(9^(12)).
To simplify this, we can use the rule of exponents that states when you multiply two numbers with the same base, you add their exponents.
In this case, the base is 9.
The first term, 9^(-3), means "9 raised to the power of -3." A negative exponent indicates the reciprocal of the base raised to the positive exponent. So, 9^(-3) is equivalent to 1/(9^3).
The second term, 9^(12), means "9 raised to the power of 12."
Now, let's simplify the expression:
(9^(-3))(9^(12)) = (1/(9^3))(9^(12))
Using the rule of adding exponents when multiplying, we can rewrite this as:
= 1/(9^(3-12))
= 1/(9^(-9))
Since a negative exponent indicates the reciprocal of the base raised to the positive exponent, we can rewrite this as:
= 1/(1/(9^9))
= 9^9
Therefore, the expression (9^(-3))(9^(12)) simplifies to 9^9.