گام به گام تمرین صفحه 89 درس 7 ریاضی هفتم (توان و جذر)

\({\left( {3 + 2} \right)^0} = {2^0} + {3^0}\)

نادرست است؛ زیرا:

\(\begin{array}{l}\left\{ \begin{array}{l}{\left( {3 + 2} \right)^0} = {\left( 5 \right)^0} = 1\\\\{2^0} + {3^0} = 1 + 1 = 2\end{array} \right.\\\\ \Rightarrow {\left( {3 + 2} \right)^0} \ne {2^0} + {3^0}\end{array}\)

\({\left( {2\frac{1}{2}} \right)^0} > {\left( { - \frac{1}{2}} \right)^2}\)

درست است؛ زیرا:

\(\begin{array}{l}\left\{ \begin{array}{l}{\left( {2\frac{1}{2}} \right)^0} = 1\\\\{\left( { - \frac{1}{2}} \right)^2} = \left( { - \frac{1}{2}} \right) \times \left( { - \frac{1}{2}} \right) = \frac{1}{4}\end{array} \right.\\\\ \Rightarrow {\left( {2\frac{1}{2}} \right)^0} > {\left( { - \frac{1}{2}} \right)^2}\end{array}\)

\({\left( { - \frac{2}{3}} \right)^0} + {\left( {\frac{1}{3}} \right)^0} > 1\)

درست است؛ زیرا:

\({\left( { - \frac{2}{3}} \right)^0} + {\left( {\frac{1}{3}} \right)^0} = 1 + 1 = 2 > 1\)

\(4 + {2^0} = 6\)

نادرست است؛ زیرا:

\(4 + {2^0} = 4 + 1 = 5 \ne 6\)

\({2^0} + {3^0} + {5^0} = 1\)

نادرست است؛ زیرا:

\({2^0} + {3^0} + {5^0} = 1 + 1 + 1 = 3 \ne 1\)

\({4^0} < {\left( { - 2} \right)^0}\)

نادرست است؛ زیرا:

\(\begin{array}{l}\left\{ \begin{array}{l}{4^0} = 1\\\\{\left( { - 2} \right)^0} = 1\end{array} \right.\\\\ \Rightarrow {4^0} = {\left( { - 2} \right)^0}\end{array}\)

الف

\(\begin{array}{l}2 \times {10^3} + 4 \times {10^2} + 7 \times {10^1} + 2 \times {10^0} = \\\\2000 + 400 + 70 + 2 = 2472\end{array}\)

\(\begin{array}{l}5 \times {10^3} + 0 \times {10^2} + 1 \times {10^1} + 9 \times {10^0} = \\\\5000 + 0 + 10 + 9 = 5019\end{array}\)

ب

\(\begin{array}{l}4235 = 4000 + 200 + 30 + 5 = \\\\4 \times 1000 + 2 \times 100 + 3 \times 10 + 5 = \\\\4 \times {10^3} + 2 \times {10^2} + 3 \times {10^1} + 5 \times {10^0}\end{array}\)

\(\begin{array}{l}9207 = 9000 + 200 + 0 + 7 = \\\\9 \times 1000 + 2 \times 100 + 0 \times 10 + 7 = \\\\9 \times {10^3} + 2 \times {10^2} + 0 \times {10^1} + 7 \times {10^0}\end{array}\)

\(\left\{ \begin{array}{l}{4^{10}} = 1,048,576\\\\{10^4} = 10000\end{array} \right. \Rightarrow {4^{10}} > {10^4}\)

با توجه به اینکه \({2^3}\) برابر است با 2×2×2 ، پس کافی است از کلیدهای ماشین حساب به صورت زیر استفاده کنیم:

\(\begin{array}{l}{a^2} - {b^2} + ab\;\;\;\;\;\;a = - 2\;\;\;b = 2\\\\{a^2} - {b^2} + ab = \\\\{( - 2)^2} - {(2)^2} + ( - 2)(2) = \\\\4 - 4 - 4 = - 4\end{array}\)

\(\begin{array}{l}{a^2} - 2{b^2} + {a^2}b\;\;\;\;\;\;a = 1\;\;\;b = - 2\\\\{a^2} - 2{b^2} + {a^2}b = \\\\{(1)^2} - 2{( - 2)^2} + {(1)^2}( - 2) = \\\\1 - 8 - 2 = - 9\end{array}\)