Which expression is correctly developed to use the Power Rule of Exponents?(1 point)
Responses
(7^8)⋅(7^10)
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
12^9
left parenthesis 12 superscript 9 baseline
The correct expression that can make use of the Power Rule of Exponents is:
(7^8)⋅(7^10)
which is written as:
left parenthesis 7 superscript 8 baseline right parenthesis times left parenthesis 7 superscript 10 baseline right parenthesis
To correctly apply the Power Rule of Exponents, we need to remember that it states:
(a^m)⋅(a^n) = a^(m+n)
Let's apply this rule to each expression:
1. (7^8)⋅(7^10):
To simplify this expression, we add the exponents of like bases (which is 7 in this case):
7^(8 + 10) = 7^18
2. (−5)^0:
According to the Power Rule of Exponents, any number raised to the power of 0 equals 1. Hence:
(−5)^0 = 1
3. (74)^8:
To apply the Power Rule of Exponents, we need to raise both the base (7) and the exponent (4) to the power of 8:
7^(4 * 8) = 7^32
4. 12^9:
This expression doesn't involve any multiplication or addition of exponents, so we can't directly apply the Power Rule of Exponents. It is already in its simplest form.
Therefore, the expression (7^8)⋅(7^10) can be correctly developed to use the Power Rule of Exponents as 7^18.