Maharashtra State Board Class 7 Maths Solutions Chapter 6 Indices Practice Set 26
Question 1.
Complete the table below:
| Sr. No. | Indices (Numbers in index form) | Base | Index | Multiplication form | Value |
| i. | 34 | 3 | 4 | 3 x 3 x 3 x 3 | 81 |
| ii. | 163 | ||||
| iii. | (-8) | 2 | |||
|
iv. |
\(\frac{3}{7} \times \frac{3}{7} \times \frac{3}{7} \times \frac{3}{7}\) | \(\frac { 81 }{ 2401 }\) | |||
| v. | (-13)4 |
Solution:
| Sr. No. | Indices (Numbers in index form) | Base | Index | Multiplication form | Value |
| i. | 34 | 3 | 4 | 3 x 3 x 3 x 3 | 81 |
| ii. | 163 | 16 | 3 | 16 x 16 x 16 | 4096 |
| iii. | (-8)² | (-8) | 2 | -8 x -8 | 64 |
|
iv. |
\(\left(\frac{3}{7}\right)^{4}\) | \(\frac { 7 }{ 7 }\) | 4 | \(\frac{3}{7} \times \frac{3}{7} \times \frac{3}{7} \times \frac{3}{7}\) | \(\frac { 81 }{ 2401 }\) |
| v. | (-13)4 | -13 | 4 | (-13) x (-13) x (-13) x (-13) | 28561 |
Question 2.
Find the value of.
i. 210
ii. 53
iii. (-7)4
iv. (-6)3
v. 93
vi. 81
vii. \(\left(\frac{4}{5}\right)^{3}\)
viii. \(\left(-\frac{1}{2}\right)^{4}\)
Solution:
i. 210
= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= 1024
ii. 53
= 5 × 5 × 5
= 125
iii. (-7)4
= (-7) × (-7) × (-7) × (-7)
= 2401
iv. (-6)3
= (-6) × (-6) × (-6)
= -216
v. 93
= 9 × 9 × 9
= 729
vi. 81
= 8
vii. \(\left(\frac{4}{5}\right)^{3}\)
\(=\frac{4}{5} \times \frac{4}{5} \times \frac{4}{5}=\frac{64}{125}\)
viii. \(\left(-\frac{1}{2}\right)^{4}\)
\(=\left(-\frac{1}{2}\right) \times\left(-\frac{1}{2}\right) \times\left(-\frac{1}{2}\right) \times\left(-\frac{1}{2}\right)=\frac{1}{16}\)