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- \( (-2)^{2}(-2)^{6}=(-2)=\square \) - \( (-6)^{2}(-6)^{2}=(-6) \square=\square \) - \( (+4)^{2}(+4)^{3}=(+4)=\square \) - \( (-1)^{7}(-1)^{8}=(-1)=\square \) - \( (+2)^{4}(+2)^{3}=(+2)=\square \) - \( (+3)^{2}(+3)^{2}=(+3)=\square \) - \( (-5)^{2}(-5)^{4}=(-5)=\square \) - \( (-7)^{2}(-7)^{1}=(-7)=\square \) - \( (-2)^{5}(-2)^{3}=(-2)=\square \) - \( (+9)^{2}(+9)^{1}=(+9)=\square \)

Ask by Owen Mills. in Ecuador
Jan 24,2025

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Tutor-Verified Answer

Answer

1. □ = 256 2. □ = 1296 3. □ = 1024 4. □ = -1 5. □ = 128 6. □ = 81 7. □ = 15625 8. □ = -343 9. □ = 256 10. □ = 729

Solution

Claro, a continuación se resuelven cada una de las expresiones y se completa el espacio en blanco (□) con el resultado correspondiente: 1. \( (-2)^{2} \cdot (-2)^{6} = (-2)^{8} = 256 \) **□ = 256** 2. \( (-6)^{2} \cdot (-6)^{2} = (-6)^{4} = 1296 \) **□ = 1296** 3. \( (+4)^{2} \cdot (+4)^{3} = (+4)^{5} = 1024 \) **□ = 1024** 4. \( (-1)^{7} \cdot (-1)^{8} = (-1)^{15} = -1 \) **□ = -1** 5. \( (+2)^{4} \cdot (+2)^{3} = (+2)^{7} = 128 \) **□ = 128** 6. \( (+3)^{2} \cdot (+3)^{2} = (+3)^{4} = 81 \) **□ = 81** 7. \( (-5)^{2} \cdot (-5)^{4} = (-5)^{6} = 15625 \) **□ = 15625** 8. \( (-7)^{2} \cdot (-7)^{1} = (-7)^{3} = -343 \) **□ = -343** 9. \( (-2)^{5} \cdot (-2)^{3} = (-2)^{8} = 256 \) **□ = 256** 10. \( (+9)^{2} \cdot (+9)^{1} = (+9)^{3} = 729 \) **□ = 729** **Resumen de los resultados:** 1. □ = 256 2. □ = 1296 3. □ = 1024 4. □ = -1 5. □ = 128 6. □ = 81 7. □ = 15625 8. □ = -343 9. □ = 256 10. □ = 729

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Extra Insights

Did you know that exponents tell you how many times to multiply a number by itself? For example, in the case of \( (-2)^2 (-2)^6 \), you simply add the exponents (2+6=8) to find that the result is equal to \( (-2)^8 \). This nifty rule simplifies calculations and helps avoid the hassle of multiplying large numbers repeatedly! When working with bases that are both positive and negative, it’s crucial to keep track of that sign. For example, \( (-1)^{7} \) gives you -1 (since it’s an odd exponent), while \( (-1)^{8} \) yields +1. So, when multiplying them together, don’t be surprised if the result flips between positive and negative! Such little details can turn a fun math problem into a tricky one if you’re not paying attention!

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