《2025年同步练习册人民教育出版社七年级数学上册人教版山东专版》

例1 把下列各式写成乘方运算的形式：
(1)$6× 6× 6× 6$； (2)$2.1× 2.1$；
(3)$(-3)× (-3)× (-3)× (-3)× (-3)$；
(4)$\dfrac{1}{2}× \dfrac{1}{2}× \dfrac{1}{2}× \dfrac{1}{2}× \dfrac{1}{2}$；
(5)$\left(-\dfrac{1}{2}\right)× \left(-\dfrac{1}{2}\right)× \left(-\dfrac{1}{2}\right)× \left(-\dfrac{1}{2}\right)$；
(6)$-\dfrac{1}{3}× \dfrac{1}{3}× \dfrac{1}{3}× \dfrac{1}{3}× \dfrac{1}{3}$.
解 (1)$6× 6× 6× 6 = 6^{4}$.
(2)$2.1× 2.1 = 2.1^{2}$.
(3)$(-3)× (-3)× (-3)× (-3)× (-3) = (-3)^{5}$.
(4)$\dfrac{1}{2}× \dfrac{1}{2}× \dfrac{1}{2}× \dfrac{1}{2}× \dfrac{1}{2} = \left(\dfrac{1}{2}\right)^{5}$.
(5)$\left(-\dfrac{1}{2}\right)× \left(-\dfrac{1}{2}\right)× \left(-\dfrac{1}{2}\right)× \left(-\dfrac{1}{2}\right) = \left(-\dfrac{1}{2}\right)^{4}$.
(6)$-\dfrac{1}{3}× \dfrac{1}{3}× \dfrac{1}{3}× \dfrac{1}{3}× \dfrac{1}{3} = -\left(\dfrac{1}{3}\right)^{5}$.

答案：
(1) $6 × 6 × 6 × 6 = 6^{4}$；
(2) $2.1 × 2.1 = 2.1^{2}$；
(3) $(-3) × (-3) × (-3) × (-3) × (-3) = (-3)^{5}$；
(4) $\frac{1}{2} × \frac{1}{2} × \frac{1}{2} × \frac{1}{2} × \frac{1}{2} = \left(\frac{1}{2}\right)^{5}$；
(5) $\left(-\frac{1}{2}\right) × \left(-\frac{1}{2}\right) × \left(-\frac{1}{2}\right) × \left(-\frac{1}{2}\right) = \left(-\frac{1}{2}\right)^{4}$；
(6) $-\frac{1}{3} × \frac{1}{3} × \frac{1}{3} × \frac{1}{3} × \frac{1}{3} = -\left(\frac{1}{3}\right)^{5}$。