Question

Write the following in index form:

(1) $\frac{7}{9}\times \frac{7}{9}\times \frac{7}{9}\times \frac{7}{9}\times \frac{7}{9}$
(2) 8 × 8 × 8
(3) m × m × m × m
(4) $\left(-\frac{5}{7}\right)\times \left(-\frac{5}{7}\right)\times ........6\mathrm{times}$
(5) $\frac{2}{3}\times \frac{2}{3}\times .........9\mathrm{times}$
(6) a × a × a × a
(7) b × b × b × ....... 10 times

Answer 1

(1) $\frac{7}{9}\times \frac{7}{9}\times \frac{7}{9}\times \frac{7}{9}\times \frac{7}{9}$
Here $\frac{7}{9}$ is multiplied 5 times.
∴ Index form of $\frac{7}{9}\times \frac{7}{9}\times \frac{7}{9}\times \frac{7}{9}\times \frac{7}{9}$ is${\left(\frac{7}{9}\right)}^5$

(2) 8 × 8 × 8
Here 8 is multiplied 3 times.
∴ Index form of 8 × 8 × 8 is (8)³

(3) m × m × m × m
Here m is multiplied 4 times.
∴ Index form of m × m × m × m is (m)⁴

(4) $\left(-\frac{5}{7}\right)\times \left(-\frac{5}{7}\right)\times ........6\mathrm{times}=\left(-\frac{5}{7}\right)\times \left(-\frac{5}{7}\right)\times \left(-\frac{5}{7}\right)\times \left(-\frac{5}{7}\right)\times \left(-\frac{5}{7}\right)\times \left(-\frac{5}{7}\right)$
Here $\left(-\frac{5}{7}\right)$ is multiplied 6 times.
∴ Index form of $\left(-\frac{5}{7}\right)\times \left(-\frac{5}{7}\right)\times \left(-\frac{5}{7}\right)\times \left(-\frac{5}{7}\right)\times \left(-\frac{5}{7}\right)\times \left(-\frac{5}{7}\right)$ is ${\left(-\frac{5}{7}\right)}^6$

(5) $\frac{2}{3}\times \frac{2}{3}\times .........9\mathrm{times}=\frac{2}{3}\times \frac{2}{3}\times \frac{2}{3}\times \frac{2}{3}\times \frac{2}{3}\times \frac{2}{3}\times \frac{2}{3}\times \frac{2}{3}\times \frac{2}{3}$
Here $\frac{2}{3}$ is multiplied 9 times.
∴ Index form of $\frac{2}{3}\times \frac{2}{3}\times \frac{2}{3}\times \frac{2}{3}\times \frac{2}{3}\times \frac{2}{3}\times \frac{2}{3}\times \frac{2}{3}\times \frac{2}{3}$is ${\left(\frac{2}{3}\right)}^9$

(6) a × a × a × a
Here a is multiplied 4 times.
∴ Index form of a × a × a × a is (a)⁴ .

(7) b × b × … 10 times = b × b × b × b × b × b × b × b × b × b
Here b is multiplied 10 times.
∴ Index form of b × b × b × b × b × b × b × b × b × b is (b)¹⁰