Question

Find the values of the following:

(1) 11³
(2) (–5)²
(3) (–3)³
(4) 10⁷
(5) 2⁴
(6) ${\left(\frac{2}{3}\right)}^5$
(7) ${\left(-\frac{1}{5}\right)}^4$
(8) 2⁸
(9) (–1)⁸
(10) (–1)⁹

Answer 1

(1) (11)³
= 11 × 11 × 11 = 1331

(2) (–5)²
= (–5) × (–5) (Product of negative sign is positive if multiplied for an even number of times)
= 25

(3) (–3)³
= (–3) × (–3) × (–3) (Product of negative sign is negative if multiplied for an odd number of times)
= –27

(4) 10⁷
= 10 × 10 × 10 × 10 × 10 × 10 × 10 = 10000000

(5) 2⁴
= 2 × 2 × 2 × 2 = 16

(6) ${\left(\frac{2}{3}\right)}^5$
$$\begin{gathered} =\left(\frac{2}{3}\right)\times \left(\frac{2}{3}\right)\times \left(\frac{2}{3}\right)\times \left(\frac{2}{3}\right)\times \left(\frac{2}{3}\right) \\ =\frac{32}{243} \end{gathered}$$

(7) ${\left(-\frac{1}{5}\right)}^4$
$=\left(-\frac{1}{5}\right)\times \left(-\frac{1}{5}\right)\times \left(-\frac{1}{5}\right)\times \left(-\frac{1}{5}\right)$ (Product of negative sign is positive if multiplied for an even number of times)
$=\frac{1}{625}$

(8) 2⁸
= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256

(9) (–1)⁸
= (–1) × (–1) × (–1) × (–1) × (–1) × (–1) × (–1) × (–1) (Product of negative sign is positive if multiplied for an even number of times)
= 1

(10) (–1)⁹
= (–1) × (–1) × (–1) × (–1) × (–1) × (–1) × (–1) × (–1) × (–1) (Product of negative sign is negative if multiplied for an odd number of times)
= –1