与えられた累乗の計算と、累乗を含む四則演算を行う問題です。 問題20は累乗の計算、問題21は累乗を含む四則演算です。

1. 問題の内容

与えられた累乗の計算と、累乗を含む四則演算を行う問題です。

問題20は累乗の計算、問題21は累乗を含む四則演算です。

2. 解き方の手順

問題20:

(1) $3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243$

(2) $(-8)^2 = (-8) \times (-8) = 64$

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

(4) $(-2.5)^2 = (-2.5) \times (-2.5) = 6.25$

(5) $0.6^3 = 0.6 \times 0.6 \times 0.6 = 0.216$

(6) $-3^4 = -(3 \times 3 \times 3 \times 3) = -81$

(7) $-(\frac{3}{5})^3 = -(\frac{3}{5} \times \frac{3}{5} \times \frac{3}{5}) = -\frac{27}{125}$

(8) $-(-7)^3 = -((-7) \times (-7) \times (-7)) = -(-343) = 343$

(9) $-(-7^2) = -( - (7 \times 7)) = -(-49) = 49$

問題21:

(1) $2 \times 3^2 = 2 \times (3 \times 3) = 2 \times 9 = 18$

(2) $4^2 \times (-3) = (4 \times 4) \times (-3) = 16 \times (-3) = -48$

(3) $(-1) \times 3^3 = (-1) \times (3 \times 3 \times 3) = (-1) \times 27 = -27$

(4) $2^2 \times (-3)^3 = (2 \times 2) \times ((-3) \times (-3) \times (-3)) = 4 \times (-27) = -108$

(5) $2^3 \times 5^3 = (2 \times 2 \times 2) \times (5 \times 5 \times 5) = 8 \times 125 = 1000$

(6) $2^3 \times (-3) \times 5 = (2 \times 2 \times 2) \times (-3) \times 5 = 8 \times (-3) \times 5 = -24 \times 5 = -120$

(7) $2 \times (-3)^2 \times 5 = 2 \times ((-3) \times (-3)) \times 5 = 2 \times 9 \times 5 = 18 \times 5 = 90$

(8) $3 \times 5 \times (-1)^2 = 3 \times 5 \times ((-1) \times (-1)) = 3 \times 5 \times 1 = 15 \times 1 = 15$

(9) $-2 \times 3^2 \times (-6)^2 = -2 \times (3 \times 3) \times ((-6) \times (-6)) = -2 \times 9 \times 36 = -18 \times 36 = -648$

(10) $(-5^2) \times 3^2 = (-(5 \times 5)) \times (3 \times 3) = (-25) \times 9 = -225$

3. 最終的な答え

問題20:

(1) 243

(2) 64

(3) $\frac{16}{81}$

(4) 6.25

(5) 0.216

(6) -81

(7) $-\frac{27}{125}$

(8) 343

(9) 49

問題21:

(1) 18

(2) -48

(3) -27

(4) -108

(5) 1000

(6) -120

(7) 90

(8) 15

(9) -648

(10) -225