問題
次の式を計算せよ.
解説
- (1) $a^{5}\times a^{2}$
- $a^{5}\times a^{2}=a^{(5+2)}$
$=$$a^{7}$
- $a^{5}\times a^{2}=a^{(5+2)}$
- (2) $3x^{2}\times4x^{4}$
- $3x^{2}\times4x^{4}=3\cdot4\cdots x^{(2+4)}$
$=$$12x^{6}$
- $3x^{2}\times4x^{4}=3\cdot4\cdots x^{(2+4)}$
- (3) $(-5xy^{2})\times3x^{2}y^{4}$
- $(-5xy^{2})\times3x^{2}y^{4}=-5\cdot3\cdot x^{(1+2)}\cdot y^{2+4}$
$=$$-15x^{3}y^{6}$
- $(-5xy^{2})\times3x^{2}y^{4}=-5\cdot3\cdot x^{(1+2)}\cdot y^{2+4}$
- (4) $(a^{3})^{4}$
- $(a^{3})^{4}=a^{(3\times4)}$
$=$$a^{12}$
- $(a^{3})^{4}=a^{(3\times4)}$
- (5) $(-a^{3})^{2}$
- $(-a^{3})^{2}=(-1)^{(1\times2)}\cdot a^{(3\times2)}$
$=$$a^{6}$
- $(-a^{3})^{2}=(-1)^{(1\times2)}\cdot a^{(3\times2)}$
- (6) $(-4a^{2}b^{2})^{3}$
- $(-4a^{2}b^{2})^{3}=(-4)^{(1\times3)}\cdot a^{(2\times3)}\cdot b^{(2\times3)}$
$=$$-64a^{6}b^{6}$
- $(-4a^{2}b^{2})^{3}=(-4)^{(1\times3)}\cdot a^{(2\times3)}\cdot b^{(2\times3)}$
- (7) $-(2x^{3})^{2}\times(-x)^{3}$
- $-(2x^{3})^{2}\times(-x)^{3}=-\{2^{(1\times2)}\cdot x^{(3\times2)}\}\cdot(-1)^{(1\times3)}\cdot x^{(1\times3)}$
$=$$4x^{9}$
- $-(2x^{3})^{2}\times(-x)^{3}=-\{2^{(1\times2)}\cdot x^{(3\times2)}\}\cdot(-1)^{(1\times3)}\cdot x^{(1\times3)}$
- (8) $2ab^{2}\times(-3a^{2}b)^{3}$
- $2ab^{2}\times(-3a^{2}b)^{3}=2ab^{2}\cdot(-3)^{(1\times3)}\cdot a^{(2\times3}\cdot b^{(1\times3)}$
$=$$-54a^{7}b^{5}$
- $2ab^{2}\times(-3a^{2}b)^{3}=2ab^{2}\cdot(-3)^{(1\times3)}\cdot a^{(2\times3}\cdot b^{(1\times3)}$
- (9) $(abc)^{2}\times(-3ab^{3}c)$
- $(abc)^{2}\times(-3ab^{3}c)=a^{2}\cdot b^{2}\cdot c^{2}\cdot(-3ab^{3}c)$
$=$$-3a^{3}b^{5}c^{3}$
- $(abc)^{2}\times(-3ab^{3}c)=a^{2}\cdot b^{2}\cdot c^{2}\cdot(-3ab^{3}c)$
