与えられた6つの計算問題を解きます。 (7) $2^5 \times (-\frac{1}{2})^4 = $ (8) $2^3 \times 3 \div 6^4 = $ (9) $(-2)^2 \div 3^2 \times (-6) = $ (10) $(-\frac{5}{6})^3 \times (-\frac{6}{5})^2 = $ (11) $(-1\frac{2}{3})^2 \times (-1\frac{1}{2})^2 = $ (12) $(-1\frac{1}{2})^4 \times (-1\frac{1}{3})^3 = $

1. 問題の内容

与えられた6つの計算問題を解きます。

(7) $2^5 \times (-\frac{1}{2})^4 =$

(8) $2^3 \times 3 \div 6^4 =$

(9) $(-2)^2 \div 3^2 \times (-6) =$

(10) $(-\frac{5}{6})^3 \times (-\frac{6}{5})^2 =$

(11) $(-1\frac{2}{3})^2 \times (-1\frac{1}{2})^2 =$

(12) $(-1\frac{1}{2})^4 \times (-1\frac{1}{3})^3 =$

2. 解き方の手順

(7)

$2^5 = 32$

$(-\frac{1}{2})^4 = \frac{1}{16}$

$32 \times \frac{1}{16} = 2$

(8)

$2^3 = 8$

$6^4 = 1296$

$8 \times 3 \div 1296 = 24 \div 1296 = \frac{24}{1296} = \frac{1}{54}$

(9)

$(-2)^2 = 4$

$3^2 = 9$

$4 \div 9 \times (-6) = \frac{4}{9} \times (-6) = -\frac{24}{9} = -\frac{8}{3}$

(10)

$(-\frac{5}{6})^3 = -\frac{125}{216}$

$(-\frac{6}{5})^2 = \frac{36}{25}$

$-\frac{125}{216} \times \frac{36}{25} = -\frac{5}{6} \times \frac{1}{6} \times \frac{6}{1} = -\frac{5}{6} \times \frac{6}{6} = -\frac{5}{6}$

(11)

$-1\frac{2}{3} = -\frac{5}{3}$

$-1\frac{1}{2} = -\frac{3}{2}$

$(-\frac{5}{3})^2 = \frac{25}{9}$

$(-\frac{3}{2})^2 = \frac{9}{4}$

$\frac{25}{9} \times \frac{9}{4} = \frac{25}{4}$

(12)

$-1\frac{1}{2} = -\frac{3}{2}$

$-1\frac{1}{3} = -\frac{4}{3}$

$(-\frac{3}{2})^4 = \frac{81}{16}$

$(-\frac{4}{3})^3 = -\frac{64}{27}$

$\frac{81}{16} \times (-\frac{64}{27}) = \frac{3}{1} \times (-\frac{4}{1}) = -12$

3. 最終的な答え

(7) 2

(8) $\frac{1}{54}$

(9) $-\frac{8}{3}$

(10) $-\frac{5}{6}$

(11) $\frac{25}{4}$

(12) -12