Indices
The index of a number says how many times to use the number in a multiplication. It is written as a small number to the right and above the base number.
Summary
The index of a number says how many times to use the number in a multiplication. It is written as a small number to the right and above the base number.
Things to Remember
- \( a^m \times a^n = a^{m+n} \)
- \( a^m ÷ a^n = a^{m - n} \)
- \( (a^m)^n = a^{mn} \)
- \( \left ( \frac {a} {b} \right ) ^m = \frac {a^m} {b^m} \)
- \( \sqrt [n] {a^m} = a^ {\frac {m} {n} } \)
- \( a^0 = 1 \)
MCQs
No MCQs found.
Subjective Questions
Q1:
What is District Development Committee?
Type: Very_short Difficulty: Easy
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Q2:
Why are DDC formed?
Type: Very_short Difficulty: Easy
Q3:
What do Illakas consist of?
Type: Very_short Difficulty: Easy
Q4:
What is the tenure of members elected for DDC?
Type: Very_short Difficulty: Easy
Q5:
Who elect member of DDC from each Illaka ?
Type: Short Difficulty: Easy
Q6:
What is parliament ?
Type: Short Difficulty: Easy
Q7:
What is council ?
Type: Short Difficulty: Easy
Q8:
What is meant by underprivileged people ?
Type: Very_short Difficulty: Easy
Q9:
What is the full form of DDC ?
Type: Short Difficulty: Easy
Q10:
What is the full form of VDC ?
Type: Very_short Difficulty: Easy
Videos
Formation of DDC
Indices
An indices is a number with the power. For example: am; a is called the base and m is the power.
In 4x3, its coefficient is 4, base is x and power is 3. The power of the base of an algebraic term is also called index. The plural form of index is indices.
Law of indices
- \( a^m \times a^n = a^{m+n} \)
- \( a^m ÷ a^n = a^{m - n} \)
- \( (a^m)^n = a^{mn} \)
- \( \left ( \frac {a} {b} \right ) ^m = \frac {a^m} {b^m} \)
- \( \sqrt [n] {a^m} = a^ {\frac {m} {n} } \)
- \( a^0 = 1 \)
- \( \left( \frac {a} {b} \right)^{-m} =\left( \frac {b} {a} \right)^m \)
- \( If \: a^m = a^n \: then, \: m = n \)
- \( a^{-m} = \frac {1}{a^m} \: (a ≠ o ) \)
- \( \left( \sqrt [n] {a} \right )^n = \left ( a^{\frac {1}{n}} \right ) ^n = a \)
- \( \sqrt [n]{a} . \sqrt [n]{b} = \sqrt [n]{ab} \)
- \( \sqrt [m]{\sqrt [n] {a}} = \sqrt [mn]{a} \)
- \( \frac {\sqrt[n]{a}}{\sqrt[n]{b}} = \sqrt[n]{\frac{a}{b}} = \left( \frac{a}{b} \right ) ^{\frac{1}{n}}\)
- \( 1^m =1 \), when 'm' is a whole number.
- \( a^x = b⇒ a = b^{\frac{1}{x}} \) [x ≠ 0]
Note:It is incorrect to write \( \sqrt{16} = \pm 4 \) because \( \sqrt{16} \) denotes the principle or positive square root of 16.
Lesson
Algebra
Subject
Compulsory Mathematics
Grade
Grade 10
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