Question

3.7*10^-9*25*10^-20/9*10^9 how to solve​

Answer 1

Given:

3.7*10^-9*25*10^-20/9*10^9.

To find:

The solution to the above problem.

Solution:

Now, to solve this question, we should aware of some properties of exponents,

If two exponents are multiplied having the same base but different powers then the powers will add and the base will remain the same.

Also,

If two exponents are divided having the same base but different powers then the powers will subtract and the base will remain the same.

${a}^{b} \times {a}^{c} = {a}^{(b + c)}$

$\frac{ {a}^{b} }{ {a}^{c} } = {a}^{(b - c)}$

So, as given, we have,

$\frac{3.7 \times {10}^{ - 9} \times 25 \times {10}^{ - 20} }{9 \times {10}^{9} }$

$= \frac{3.7 \times 25 \: \times {10}^{ - 9 + ( - 20)} }{9 \times {10}^{9} }$

$= \frac{92.5 \times {10}^{ - 29} }{9 \times {10}^{9} }$

$= {10.27 \times {10}^{ (- 29 - \: 9)} }$

$= {10.27 \times {10}^{ - 38} }$

Hence, the answer to the given problem 3.7*10^-9*25*10^-20/9*10^9 is 10.27 × 10^-38.