جواب کار در کلاس صفحه ۶۳ ریاضی نهم

الف)
\[\frac{7^3}{7^5} = 7^{3-5} = 7^{-2}\]

ب)
\[2^{-2} \times 5^{-2} = (2 \times 5)^{-2} = 10^{-2}\]

پ)
\[\left(\frac{-2}{3}\right)^{-3} \times 12^{-3} = \left(\frac{-3}{2}\right)^{3} \times \left(\frac{1}{12}\right)^{3} = \left(\frac{-3}{2} \times \frac{1}{12}\right)^{3} = \left(\frac{-3}{24}\right)^{3} = \left(-\frac{1}{8}\right)^{3}\]

ت)
\[\left[\left(-\frac{2}{5}\right)^{-2}\right]^{-1} = \left(-\frac{2}{5}\right)^{(-2)(-1)} = \left(-\frac{2}{5}\right)^{2}\]

ث)
\[\frac{2^8 \times 5^{10}}{2^4 \times 5^6} = 2^{8-4} \times 5^{10-6} = 2^4 \times 5^4 = (2 \times 5)^4 = 10^4\]

ج)
\[\frac{x^5 \cdot y^2 \cdot z}{x^{-2} \cdot y^7 \cdot z^3} = x^{5-(-2)} \cdot y^{2-7} \cdot z^{1-3} = x^{7} \cdot y^{-5} \cdot z^{-2} \qquad (x,y,z \neq 0)\]