Which expression is correctly developed to use the Power Rule of Exponents?
1. 12^9
2. (-5)^0
3. (7^4)^8
4. (7^8) * ( 7^10)
The expression that is correctly developed to use the Power Rule of Exponents is:
4. (7^8) * (7^10)
The correct expression to use the Power Rule of Exponents is the third option, (7^4)^8.
The Power Rule of Exponents states that when you have a base raised to an exponent, and that expression is raised to another exponent, you multiply the exponents. So, let's go through each option to see which one correctly follows this rule.
1. 12^9: This expression does not involve multiple exponents, so it does not require the Power Rule of Exponents.
2. (-5)^0: The Power Rule of Exponents is not applicable here because the exponent is 0. Any non-zero number raised to the power of 0 is always equal to 1. So, (-5)^0 = 1.
3. (7^4)^8: This expression correctly applies the Power Rule of Exponents. To simplify it, you multiply the exponents: 7^(4*8) = 7^32.
4. (7^8) * (7^10): This expression involves multiplying two terms with the same base, so the Power Rule of Exponents can be applied. To simplify it, you add the exponents: 7^(8+10) = 7^18.
Therefore, the expression that correctly uses the Power Rule of Exponents is option 4: (7^8) * (7^10).