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Which expression is correctly developed to use the Power Rule of Exponents?(1 point)
(−5)0
12^9
(7^4)8
(7^8)⋅(7^10)
(7^8)⋅(7^10)
To correctly apply the Power Rule of Exponents, we need to remember that the rule states that when raising a power to another power, we multiply the exponents.
Let's apply the Power Rule of Exponents to each expression:
1) (-5)^0:
The Power Rule of Exponents is applied by multiplying the exponents. In this case, since the exponent is 0, any non-zero number raised to the power of 0 is equal to 1. So, (-5)^0 = 1.
2) 12^9:
There is no need to apply the Power Rule of Exponents in this expression because there is no exponent being raised to another power. So, 12^9 remains as it is.
3) (7^4)^8:
To simplify this expression, we apply the Power Rule of Exponents, which requires us to multiply the exponents. So, (7^4)^8 = 7^(4*8) = 7^32.
4) (7^8)⋅(7^10):
To simplify this expression, we again apply the Power Rule of Exponents by multiplying the exponents. So, (7^8)⋅(7^10) = 7^(8+10) = 7^18.
To summarize, the correctly developed expressions using the Power Rule of Exponents are:
1) (-5)^0 = 1
2) 12^9
3) (7^4)^8 = 7^32
4) (7^8)⋅(7^10) = 7^18