Final answer:
The simplified form of the expression m⁷(m²)⁻⁹ is m⁻¹¹, found by applying exponent rules and combining the exponents with the same base.
Step-by-step explanation:
The student asked about simplifying the expression m⁷(m²)⁻⁹. To simplify this expression, we need to apply the rules of exponents. When we multiply two exponential expressions with the same base, we add the exponents. However, when there is a negative exponent, it indicates the reciprocal of the base raised to the positive of that exponent.
So in this case, (m²)⁻⁹ would be the same as m⁻¹⁸. Now, we combine m⁷ and m⁻¹⁸ by adding the exponents (7 + (-18)) to get m⁻¹¹. Therefore, the simplified form of the expression is m⁻¹¹.