Which expression is correctly developed to use the Power Rule of Exponents?(1 point)
Responses
129
12 superscript 9 baseline
(78)⋅(710)
left parenthesis 7 superscript 8 baseline right parenthesis times left parenthesis 7 superscript 10 baseline right parenthesis
(−5)0
left parenthesis negative 5 right parenthesis superscript 0 baseline
(74)8
left parenthesis 7 superscript 4 baseline right parenthesis superscript 8 baseline
To correctly use the Power Rule of Exponents, we need to follow the rule that states "To raise a power to a power, multiply the exponents."
Using this rule, we can evaluate the expression (74)8 as follows:
7^4 raised to the power of 8 is equal to (7^4)^8.
To simplify this further, we multiply the exponents: 4 * 8 = 32.
Therefore, the expression (74)8 can be written as 7^32.
To correctly use the Power Rule of Exponents, the expression should be in the form of a base raised to a power.
The Power Rule states that when a base is raised to an exponent, and then that result is raised to another exponent, we can simply multiply the exponents together.
Let's analyze the given expressions one by one:
1. 129
This expression does not have a base raised to a power. It is simply a number without any exponent. Therefore, it does not use the Power Rule of Exponents.
2. 12^9
This expression follows the Power Rule of Exponents. The base is 12 raised to the power of 9, which can be written as 12^9. This is the correct use of the Power Rule.
3. (78)⋅(710)
This expression does not have a base raised to a power. It is a multiplication of two numbers: 78 and 710. Therefore, it does not use the Power Rule of Exponents.
4. (−5)^0
This expression follows the Power Rule of Exponents. The base is -5 raised to the power of 0, which can be written as (-5)^0. This is the correct use of the Power Rule.
5. (74)8
This expression does not follow the Power Rule of Exponents. It is a number 74 raised to the power of 8 without parentheses, which makes it unclear whether the entire expression is the base or if only the "4" is the base. To correctly use the Power Rule, the base and exponent should be clearly indicated.
Therefore, the expression correctly developed to use the Power Rule of Exponents is 12^9.