Final answer:
Solving the expressions provided by the student requires a correct application of exponent rules and might include calculating each exponent separately, multiplying like bases, and expressing large numbers or those involved in divisions in scientific notation.
Step-by-step explanation:
The student's question involves solving a series of equations and expressions, where exponents play a significant role. When you attempt to solve these types of problems, make sure you correctly apply the rules of exponents, which can often include multiplying like bases and determining the power of a power. For example, when you are given the expression (15^3) * (6^9), you should calculate each exponent separately and then multiply the results. Sometimes it's easier to rewrite the numbers, especially large ones, or those involved in divisions, in scientific notation before proceeding.
Here are some general tips: Remember that when you raise a power to another power, like ((-2)^5)^8, you multiply the exponents. Also, when evaluating expressions in scientific notation, be sure to apply the exponent to all parts of the base number. For simplicity and convenience, a calculator can be used to directly compute these expressions or to convert numbers to and from scientific notation.