Answer:
The standard form of [tex]\frac{6 \times 10^{2}}{3 \times 10^{-5}}[/tex] is 20,00,0000
Solution:
Given that [tex]\frac{6 \times 10^{2}}{3 \times 10^{-5}}[/tex] ---- eqn 1
To write[tex]\frac{6 \times 10^{2}}{3 \times 10^{-5}}[/tex] in standard form,
We know that [tex]\bold{\frac{1}{a^{-m}} = a^{m}}[/tex] .So [tex]\frac{1}{10^{-5}}[/tex] becomes [tex]10^{5}[/tex].
Now eqn 1 becomes,
[tex] = \frac{6 \times 10^{2}}{3} \times 10^{5}[/tex] ----- eqn 2
We know that [tex]\bold{a^{m} \times a^{n}=a^{m+n}}[/tex], so [tex]10^{2} \times 10^{5} = 10^{7}[/tex]
Now eqn 2 becomes,
[tex]= \frac{6}{3} \times 10^{7}[/tex]
[tex]= 2 \times 10^{7}[/tex] ---- eqn 3
Expanding [tex]10^{7}[/tex]:
Here 10 is the base term and 7 is the exponent value. So base term 10 is multiplied by itself 7 times.
[tex]10^{7} = 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10[/tex]
Now eqn 3 becomes,
[tex]= 2 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10[/tex]
= 20,00,0000
Hence the standard form of [tex]\frac{6 \times 10^{2}}{3 \times 10^{-5}}[/tex] is 20,00,0000
