Question
An expression was simplified to 24^12. which expression correctly used the Product Rule of Exponents to simplify?
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GPT 3.5
The Product Rule of Exponents states that when multiplying two expressions with the same base, you keep the base and add the exponents.
To simplify the expression, we need to find a way to rewrite it as a product. One way to do this is by using a power of 1 as a factor.
The expression 24^12 can be written as:
(2^3 * 3^1)^12
Now, we can apply the Product Rule of Exponents to simplify:
(2^3 * 3^1)^12 = 2^(3*12) * 3^(1*12)
= 2^36 * 3^12
Therefore, the expression that correctly uses the Product Rule of Exponents to simplify is 2^36 * 3^12.
To simplify the expression, we need to find a way to rewrite it as a product. One way to do this is by using a power of 1 as a factor.
The expression 24^12 can be written as:
(2^3 * 3^1)^12
Now, we can apply the Product Rule of Exponents to simplify:
(2^3 * 3^1)^12 = 2^(3*12) * 3^(1*12)
= 2^36 * 3^12
Therefore, the expression that correctly uses the Product Rule of Exponents to simplify is 2^36 * 3^12.
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