Apply the properties of integer exponents to generate an equivalent algebraic expression to 3x^3 y^−412x^7y^4 .(1 point) Responses 4x^4y^8 x superscript 4 baseline y superscript 8 baseline 14x12 Start Fraction 1 over 4 x superscript 12 baseline 14x4y8 Start Fraction 1 over 4 x superscript 4 baseline y superscript 8 baseline 312x4y8

Question

Apply the properties of integer exponents to generate an equivalent algebraic expression to 3x^3 y^−412x^7y^4 .(1 point) Responses 4x^4y^8  x superscript 4 baseline y superscript 8 baseline 14x12 Start Fraction 1 over 4 x superscript 12 baseline 14x4y8 Start Fraction 1 over 4 x superscript 4 baseline y superscript 8 baseline 312x4y8

GPT-4o mini · Answer

To simplify the expression $3x^3 y^{-4} \cdot 12x^7y^4$, we will use the properties of integer exponents. 1. **Multiply the coefficients**: $$ 3 \cdot 12 = 36. $$ 2. **Combine the $x$ terms**: $$ x^3 \cdot x^7 = x^{3+7} = x^{10}. $$ 3. **Combine the $y$ terms**: $$ y^{-4} \cdot y^4 = y^{-4+4} = y^0 = 1. $$ Putting it all together, we get: $$ 36x^{10} \cdot 1 = 36x^{10}. $$ Since none of the suggested responses match $36x^{10}$, it seems there may be a misunderstanding. However, if the problem involves further operations not shown in the provided information, please clarify. If you want calculations with specific values or forms in mind, feel free to ask! Otherwise, the simplified version based on provided data remains $36x^{10}$.