Maharashtra Board Class 7 Chapter 6 Set 26 Indices Solutions

Question 1. Complete the table below:

Answer:

In simple words: This table demonstrates the components of an index form, including the base, index (exponent), the expanded multiplication form, and the final value. Each row illustrates how to convert between these forms.

🎯 Exam Tip: Pay close attention to negative bases and fractions when expanding indices, as signs and fractional multiplication rules are common areas for errors.

Question 2. Find the value of.
(i) \(2^{10}\)
(ii) \(5^3\)
(iii) \( (-7)^4 \)
(iv) \( (-6)^3 \)
(v) \(9^3\)
(vi) \(8^1\)
(vii) \( (\frac{4}{5})^3 \)
(viii) \( (\frac{-1}{2})^4 \)
Answer:
(i) \(2^{10}\)
\( = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \)
\( = 1024 \)
(ii) \(5^3\)
\( = 5 \times 5 \times 5 \)
\( = 125 \)
(iii) \( (-7)^4 \)
\( = (-7) \times (-7) \times (-7) \times (-7) \)
\( = 2401 \)
(iv) \( (-6)^3 \)
\( = (-6) \times (-6) \times (-6) \)
\( = -216 \)
(v) \(9^3\)
\( = 9 \times 9 \times 9 \)
\( = 729 \)
(vi) \(8^1\)
\( = 8 \)
(vii) \( (\frac{4}{5})^3 \)
\( = \frac{4}{5} \times \frac{4}{5} \times \frac{4}{5} = \frac{64}{125} \)
(viii) \( (\frac{-1}{2})^4 \)
\( = (\frac{-1}{2}) \times (\frac{-1}{2}) \times (\frac{-1}{2}) \times (\frac{-1}{2}) = \frac{1}{16} \) In simple words: To find the value of a number in index form, multiply the base by itself as many times as indicated by the index. For negative bases, an even index results in a positive value, while an odd index results in a negative value.

🎯 Exam Tip: Remember that any number raised to the power of 1 is the number itself. Also, correctly applying the sign rules for negative bases is crucial for accurate answers.