Which expression is correctly developed to use the power rule of exponents
(-5)0
(7 8) - (7 10)
(7 4)8
12 8
The correct expression that uses the power rule of exponents is (7^4)^8.
The expression that is correctly developed to use the power rule of exponents is (7^4)^8.
To correctly use the power rule of exponents, we need to understand the rule itself. The power rule states that when raising a power to another power, we need to multiply the exponents.
Now let's analyze each expression and apply the power rule:
1. (-5)^0:
The expression (-5)^0 is an example of raising a number to the power of zero. According to the power rule, any number (except 0) raised to the power of zero is equal to 1. Therefore, (-5)^0 equals 1.
2. (7^8) - (7^10):
This expression involves subtracting two exponential terms. We can simplify this using the power rule by keeping the base the same (which is 7 in this case) and subtracting the exponents. Hence, we have 7^(8-10) = 7^(-2).
3. (7^4)^8:
In this expression, we have a power raised to another power. Using the power rule, we multiply the exponents together. So, (7^4)^8 becomes 7^(4*8) = 7^32.
4. 12^8:
Since there is no operation or another exponent involved, this expression doesn't require the power rule. It is simply 12 raised to the power of 8, which is written as 12^8.
To summarize:
1. (-5)^0 = 1
2. (7^8) - (7^10) = 7^(-2)
3. (7^4)^8 = 7^32
4. 12^8 remains as 12^8.