Which expression is correctly developed to use the Power Rule of Exponents? (1 point)
(7 ^ 8)(7 ^ 10)
(- 5) ^ 0
(7 ^ 4) ^ 8
12 ^ 9
(7 ^ 8)(7 ^ 10)
is the bot right?
The expression that is correctly developed to use the Power Rule of Exponents is:
(7^8)(7^10)
The Power Rule of Exponents states that when you have an exponent raised to another exponent, you multiply the exponents together.
Let's analyze the given expressions to see which one correctly applies the Power Rule of Exponents.
1. (7 ^ 8)(7 ^ 10):
In this expression, we have two expressions with the same base (7). To multiply them, we need to apply the Power Rule of Exponents by adding the exponents: 7^(8+10) = 7^18. So the expression (7 ^ 8)(7 ^ 10) can be correctly simplified as 7^18.
2. (-5) ^ 0:
In this expression, we have a base of -5 raised to the exponent 0. According to the Power Rule of Exponents, any number (except 0) raised to the power of 0 will always equal 1. Therefore, (-5) ^ 0 is correctly simplified as 1.
3. (7 ^ 4) ^ 8):
In this expression, we have an expression (7 ^ 4) raised to the power of 8. To correctly simplify this expression, we need to apply the Power Rule of Exponents by multiplying the exponents: (7^4)^8 = 7^(4*8) = 7^32. So the expression (7 ^ 4) ^ 8 can be simplified as 7^32.
4. 12 ^9:
In this expression, we have a base of 12 raised to the exponent 9. There is no indication of another exponent to apply the Power Rule of Exponents, so this expression is already fully simplified.
Therefore, the expression that correctly applies the Power Rule of Exponents is (7 ^ 4) ^ 8.