Which expression is correctly developed to use the Power Rule of Exponents?
Responses
12^9
(7^8)⋅(7^10)
(−5)^0
(7^4)^8
The expression that correctly utilizes the Power Rule of Exponents is:
(7^4)^8
can you explain
Certainly!
The Power Rule of Exponents states that when you raise a power to another power, you multiply the exponents. In other words, if you have an expression of the form (a^b)^c, the result can be simplified to a^(b*c).
In the given expression, (7^4)^8, we have a base of 7 raised to the power of 4, and that entire result is then raised to the power of 8.
To apply the Power Rule of Exponents, we can multiply the exponents 4 and 8:
7^(4*8) = 7^32
So, the expression (7^4)^8 simplifies to 7^32 using the Power Rule of Exponents.
The expression that correctly uses the Power Rule of Exponents is (7^4)^8.
The expression that correctly utilizes the Power Rule of Exponents is:
(7^4)^8
To understand the Power Rule of Exponents, we first need to recall the basic rule: when we raise a base to an exponent, we multiply the base by itself as many times as the exponent indicates.
The Power Rule of Exponents tells us that when we have a power of a power, we multiply the exponents. In other words, (a^m)^n is equal to a^(m * n).
In the given expression, we have (7^4)^8. According to the Power Rule, we can multiply the exponents 4 and 8 together to simplify the expression. So, (7^4)^8 can be rewritten as 7^(4 * 8) or 7^32. Therefore, the expression (7^4)^8 is correctly developed to use the Power Rule of Exponents.