The expression
is equivalent to
. (option C)
How to determine the equivalent expression?
The expression given is
, and when simplified, it becomes:
![\[ 7^(-8) * 7^3 \]](https://img.qammunity.org/2020/formulas/mathematics/middle-school/1l5djcsncpwj1f2mzz9xpvkj9gi6gnkizc.png)
Using the properties of exponents, we can combine these terms:
![\[ 7^(-8 + 3) = 7^(-5) \]](https://img.qammunity.org/2020/formulas/mathematics/middle-school/xpzdcsm3ul1hrbqdqgawf451zmxycdodyx.png)
So, the expression
is equivalent to
.
The properties of exponents are fundamental rules or laws that govern the manipulation, simplification, and calculation of expressions involving exponents. These properties are essential in algebra and arithmetic, allowing for the efficient simplification and evaluation of exponential expressions.