《2025年同步轻松练习七年级数学上册人教版》

例2 计算：
(1)$(-2)^{3}$；(2)$-2^{4}$；(3)$(-0.2)^{3}$；(4)$\left(-1\dfrac{1}{3}\right)^{3}$.

答案： 解
(1)$(-2)^{3} = (-2)× (-2)× (-2) = -8$.
(2)$-2^{4} = -2× 2× 2× 2 = -16$.
(3)$(-0.2)^{3} = (-0.2)× (-0.2)× (-0.2) = -0.008$.
(4)$\left(-1\dfrac{1}{3}\right)^{3} = \left(-\dfrac{4}{3}\right)× \left(-\dfrac{4}{3}\right)× \left(-\dfrac{4}{3}\right) = -\dfrac{64}{27}$.

例3 计算：
(1)$(-3)^{4}$； (2)$\left(-\dfrac{1}{2}\right)^{5}$； (3)$-3^{4}$.

答案： 解
(1)$(-3)^{4} = 3^{4} = 3× 3× 3× 3 = 81$.
(2)$\left(-\dfrac{1}{2}\right)^{5} = -\left(\dfrac{1}{2}\right)^{5} = -\left(\dfrac{1}{2}× \dfrac{1}{2}× \dfrac{1}{2}× \dfrac{1}{2}× \dfrac{1}{2}\right) = -\dfrac{1}{32}$.
(3)$-3^{4} = -(3× 3× 3× 3) = -81$.

例4 计算：(1)$-1^{3} - (-4)^{2} ÷ 8× \left(-\dfrac{1}{4}\right)$；
(2)$6^{2}× \left(-\dfrac{1}{4} + \dfrac{2}{9}\right) - (-16)÷ 8$.

答案：
(1) $-1^{3} - (-4)^{2} ÷ 8× \left(-\dfrac{1}{4}\right)$
$=-1 - 16 ÷ 8× \left(-\dfrac{1}{4}\right)$
$=-1 - 2× \left(-\dfrac{1}{4}\right)$
$=-1 + \dfrac{1}{2}$
$=-\dfrac{1}{2}$
(2) $6^{2}× \left(-\dfrac{1}{4} + \dfrac{2}{9}\right) - (-16)÷ 8$
$=36× \left(-\dfrac{9}{36} + \dfrac{8}{36}\right) + 2$
$=36× \left(-\dfrac{1}{36}\right) + 2$
$=-1 + 2$
$=1$