Question

Write the meaning of a° & a⁻ᵐ
Ans also the laws of indices; no spam

Answer 1

$\Large{\underbrace{\sf{\red{Required \; Solution:}}}}$

Write the meaning of a°

Answer:

• a° = 1

Explanation:

If a ≠ 0

$\sf{Then, \; \dfrac{a^m}{a^m}=1}$

   

$\sf{Also, \; \dfrac{ a^m }{ a^m } = a^{m-m} = a^\circ}$

     

$\therefore \; \boxed{\sf{\orange{a^\circ = 1}}}$

   

Write the meaning of a⁻ᵐ

Answer:

• aᵐ = ¹/ₐᵐ

Explanation:

$\implies \sf{a^{-m} = a^{-m} \times 1}$

   

$\implies \sf{ a^{-m} \times \cfrac{ a^m }{ a^m } }$

   

$\implies \sf{ \cfrac{ a^{ -m+m }}{ a^m } }$

   

$\implies \sf{ \cfrac{ a^0 }{ a^m } = \cfrac{ 1 }{ a^m } }$

   

$\therefore \; \boxed{\sf{\orange{a^{-m} = \dfrac{ 1 }{ a^m }}}}$

     

⋆ Laws of Indices;

Remember: If a is a non-zero and m and n are integers, then

• Law 1 - $\sf{a^m \times a^n = a^{m+n}}$

• Law 2 - $\sf{ a^m \div a^n = a^{m-n} }$

• Law 3 - $\sf{a^1 = a}$

• Law 4 - $\sf{a^0 = 1}$

• Law 5 - $\sf{a^{-m} = \dfrac{ 1 }{ a^m } }$

• Law 6 - $\sf{ (ab)^m = a^m \times b^m }$

• Law 7 - $\sf{ \bigg( \dfrac{a}{b} \bigg)^m = \dfrac{a^m}{b^m} }$

• Law 8 - $\sf{(a^m)^n = a^{mn}}$

• Law 9 - $\sf{ \bigg( \dfrac{a}{b} \bigg)^{-m} = \bigg( \dfrac{b}{a} \bigg)^m }$

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Answer 2

Answer:

1. a° = 1
2. a⁻ᵐ = 1/aᵐ

Step-by-step explanation:

1. Solution;

If a ≠ 0

Then aᵐ/aᵐ = aᵐ⁻ⁿ = a°

∴ a° = 1

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1. Solution;

a⁻ᵐ = 1

= a⁻ᵐ ×  aᵐ/aᵐ

=  a⁻ᵐ⁺ⁿ/aᵐ

= a⁰/aᵐ = 1/aᵐ

∴ a⁻ᵐ = 1/aᵐ

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✦ 「Law of exponents」

-› $\sf{a^m \times a^n = a^{m+n}}$

-› $\sf{ a^m \div a^n = a^{m-n} }$

-› $\sf{a^1 = a}$

-› $\sf{a^0 = 1}$

-› $\sf{a^{-m} = \dfrac{ 1 }{ a^m } }$

-› $\sf{ (ab)^m = a^m \times b^m }$

-› $\sf{ \bigg( \dfrac{a}{b} \bigg)^m = \dfrac{a^m}{b^m} }$

-› $\sf{(a^m)^n = a^{mn}}$

-› $\sf{ \bigg( \dfrac{a}{b} \bigg)^{-m} = \bigg( \dfrac{b}{a} \bigg)^m }$

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