Final answer:
To simplify m^9 ÷ m^{-3}, we subtract the exponents, yielding m^{12}. The correct answer is not listed among the provided options, indicating an error in the question or options.
Step-by-step explanation:
To simplify the expression \( m^9 \div m^{-3} \), we use the properties of exponents. Specifically, when dividing two expressions with the same base, you subtract the exponents.
The expression \( m^9 \div m^{-3} \) involves the base \( m \) with two different exponents. To simplify it, we follow this rule: \( m^a \div m^b = m^{(a-b)} \) Applying this rule to our expression: \( m^9 \div m^{-3} = m^{(9 - (-3))} \) Now, when subtracting a negative number, it is the same as adding its positive equivalent.
Therefore: \( m^{(9 - (-3))} = m^{(9 + 3)} \) This simplifies further to: \( m^{12} \) Hence, the simplified form of the given expression is \( m^{12} \), which corresponds to option (a)The question asks us to simplify the expression m^9 ÷ m^{-3}. When dividing expressions with the same base, we subtract the exponents according to the laws of exponents. So, m^9 ÷ m^{-3} = m^{9 - (-3)} = m^{9 + 3} = m^{12}.
The correct answer is not in the options provided, thus it seems there is an error in the multiple-choice answers. Please double-check the question and provided options. If the question is indeed as given, none of the options (a) -m^12, (b) m^{-6}, (c) m^6, or (d) m^{27} is correct. The correct answer should be m^{12}.