im sorry i did it wrong :(
If the expression (2^3)^2 was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression? (1 point)
A. (2x2x2) x (2x2x2)
B. (2)^5
C. (2x2)
D. 6
The correct expanded equivalent expression using the Power Rule of Exponents would be:
A. (2x2x2) x (2x2x2)
To simplify the expression (2^3)^2 using the Power Rule of Exponents, we follow the rule which states that when a power is raised to another power, we multiply the exponents.
So, (2^3)^2 can be simplified as 2^(3x2) or 2^6.
Therefore, the expanded equivalent expression is (2)^6.
The correct answer is B. (2)^5 is not the correct expanded equivalent expression.
No problem at all! Let's work through this together.
To simplify the expression (2^3)^2 using the Power Rule of Exponents, we first need to understand the rule. The Power Rule of Exponents states that when raising an exponent to another exponent, we multiply the exponents.
In this case, we have (2^3)^2. The first exponent is 3, and we want to raise that to the power of 2. So we multiply 3 by 2:
2^3 x 2^3 = 2^(3+3) = 2^6
Now, let's look at the options:
A. (2x2x2) x (2x2x2)
This option represents the expanded form of (2^3)^2, but it is not the correct answer according to the Power Rule of Exponents.
B. (2)^5
This option does not match the result we obtained from simplifying (2^3)^2 using the Power Rule of Exponents.
C. (2x2)
This option represents 2^2, which is not the same as (2^3)^2. Therefore, it is not the correct answer.
D. 6
This option does not match the result we obtained from simplifying (2^3)^2 using the Power Rule of Exponents.
So, in this case, the correct answer would be B. (2)^5, as it represents the expanded equivalent expression of (2^3)^2 after applying the Power Rule of Exponents.