Respuesta :
Answer:
1. [tex]2 \times 10^{- 4} = 2 \div 10^{4}[/tex]
2. [tex](- 10)^{2} = 100[/tex] and [tex]- 10^{2} = - 100[/tex]
3. [tex](a.b.c. ........)^{n} = a^{n}.b^{n}.c^{n}. ..........[/tex]
Example: [tex](30)^{4} = (2 \times 3 \times 5)^{4} = 2^{4} \times 3^{4} \times 5^{4}[/tex]
Step-by-step explanation:
1. We have [tex]2 \times 10^{- 4}[/tex], and we have to prove that this term is equivalent to [tex]2 \div 10^{4}[/tex].
Now, [tex]2 \times 10^{- 4}[/tex]
= [tex]2 \times \frac{1}{10^{4} }[/tex]
{Since we know the property of exponent as [tex]a^{- b} = \frac{1}{a^{b} }[/tex] }
= [tex]\frac{2}{10^{4} }[/tex]
= [tex]2 \div 10^{4}[/tex]
2. [tex](- 10)^{2} = (- 10) \times (- 10) = 100[/tex] and
[tex]- 10^{2} = - [(10) \times (10)] = - 100[/tex]
3. The power of products property gives
[tex](a.b.c. ........)^{n} = a^{n}.b^{n}.c^{n}. ..........[/tex] ........ (1)
For example, we can write, [tex](30)^{4} = (2 \times 3 \times 5)^{4} = 2^{4} \times 3^{4} \times 5^{4} = 810000[/tex]
