Questions: M^2 * a^12 / 1 * 1 / M^3 a^2

Solution Steps

To simplify the given expression, we need to apply the laws of exponents. Specifically, we will subtract the exponents of like bases in the numerator and the denominator. For the base \( M \), we subtract the exponent in the denominator from the exponent in the numerator. Similarly, for the base \( a \), we subtract the exponent in the denominator from the exponent in the numerator.

We start with the expression:

\[ \frac{M^{2} \cdot a^{12}}{M^{3} \cdot a^{2}} \]

Using the laws of exponents, we simplify the expression by subtracting the exponents of like bases:

1. For the base \( M \): \[ M^{2} / M^{3} = M^{2-3} = M^{-1} \]

2. For the base \( a \): \[ a^{12} / a^{2} = a^{12-2} = a^{10} \]

Combining the results from the previous step, we have:

\[ \frac{a^{10}}{M} \]

Final Answer