An expression was simplified to 24^12. which expression correctly used the Product Rule of Exponents to simplify?
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 an expression using the Product Rule of Exponents, we need to multiply the exponents.
The Product Rule of Exponents states that for any positive base, like 24, and any positive exponents, like 12, if the same base is being multiplied, we can add the exponents together.
In this case, to simplify the expression to 24^12, we need to find the original expression where the exponents were added together.
Let's assume the original expression was 24^6 * 24^6.
To simplify this expression using the Product Rule of Exponents, we add the exponents 6 + 6:
24^6 * 24^6 = 24^(6 + 6)
Simplifying the exponent, we have:
24^(12)
So, the expression that correctly used the Product Rule of Exponents to simplify is 24^6 * 24^6 = 24^(12).
To simplify an expression using the Product Rule of Exponents, you need to multiply repeated factors with the same base. The Product Rule states that when you multiply two exponential expressions with the same base, you add their exponents.
In this case, the simplified expression is 24^12. To find the original expression that was simplified, we need to look for factors with the same base, 24, and add their exponents.
Let's consider some possible options:
1. 4^6 * 6^6
2. 3^4 * 8^3
3. (2^3)^4
To determine which expression correctly uses the Product Rule and simplifies to 24^12, we can evaluate each option to see if it matches.
1. 4^6 * 6^6 evaluates to (4 * 4 * 4 * 4 * 4 * 4) * (6 * 6 * 6 * 6 * 6 * 6) = 2,097,152. This is not equal to 24^12.
2. 3^4 * 8^3 evaluates to (3 * 3 * 3 * 3) * (8 * 8 * 8) = 9,216. This is also not equal to 24^12.
3. (2^3)^4 evaluates to (2 * 2 * 2 * 2) * (2 * 2 * 2 * 2) * (2 * 2 * 2 * 2) * (2 * 2 * 2 * 2) = 65,536.
Therefore, the expression that correctly uses the Product Rule of Exponents to simplify to 24^12 is option 3: (2^3)^4.