Question

PLZ HELP ME WILL GIVE BRAINLIEST

Answer 1

Answer:

1.  $2 \times 10^{- 4} = 2 \div 10^{4}$

2. $(- 10)^{2} = 100$ and $- 10^{2} = - 100$

3. $(a.b.c. ........)^{n} = a^{n}.b^{n}.c^{n}. ..........$

Example:  $(30)^{4} = (2 \times 3 \times 5)^{4} = 2^{4} \times 3^{4} \times 5^{4}$

Step-by-step explanation:

1. We have $2 \times 10^{- 4}$, and we have to prove that this term is equivalent to $2 \div 10^{4}$.

Now, $2 \times 10^{- 4}$

= $2 \times \frac{1}{10^{4} }$  

{Since we know the property of exponent as $a^{- b} = \frac{1}{a^{b} }$ }

= $\frac{2}{10^{4} }$

= $2 \div 10^{4}$

2. $(- 10)^{2} = (- 10) \times (- 10) = 100$ and  

$- 10^{2} = - [(10) \times (10)] = - 100$

3. The power of products property gives

$(a.b.c. ........)^{n} = a^{n}.b^{n}.c^{n}. ..........$ ........ (1)

For example, we can write, $(30)^{4} = (2 \times 3 \times 5)^{4} = 2^{4} \times 3^{4} \times 5^{4} = 810000$