Final answer:
The power to a power rule is used to simplify expressions where an exponent has another exponent next to it by multiplying the exponents. This rule helps to understand the inverse relationship between the magnitude of a number and the size of its exponent, as well as to simplify the multiplication of exponentials by adding their exponents.
Step-by-step explanation:
An exponent with another exponent right next to it uses the power to a power rule to simplify the expression. In mathematical terms, when you have an expression like (an)m, you would multiply the exponents together to simplify. This would result in an*m. For instance, (32)3 would be simplified to 32*3, which equals 36.
The power to a power rule not only simplifies calculations, but it also clarifies the relation between exponents and magnitudes. As the number N decreases in magnitude, the exponent increases, which demonstrates an inverse relationship. Similarly, in multiplication of exponentials, you multiply the digit terms and add the exponents of the exponential terms, as shown in the equation 3.2 × 103 × 2 × 102 simplifying to 6.4 × 105.