Question

How do you simplify $\dfrac{{{10}^{4}}}{{{10}^{-2}}}$ ?

Answer 1

Hint: We can apply the exponential formula $\dfrac{{{a}^{n}}}{{{a}^{m}}}={{a}^{n-m}}$ to solve the problem. We can see that question is the same format as the formula. In $\dfrac{{{10}^{4}}}{{{10}^{-2}}}$ the value of a is 10 , the value of n is 4 and the value of n is -2. We can replace these in the formula and solve the problem.

Complete step by step answer:
We know the exponential property $\dfrac{{{a}^{n}}}{{{a}^{m}}}={{a}^{n-m}}$ where a is not equal to 0.
We can apply the above formula to solve $\dfrac{{{10}^{4}}}{{{10}^{-2}}}$ . By applying the above formula we get
$\Rightarrow \dfrac{{{10}^{4}}}{{{10}^{-2}}}={{10}^{4-\left( -2 \right)}}$
Further solving we get
$\Rightarrow \dfrac{{{10}^{4}}}{{{10}^{-2}}}={{10}^{6}}$
${{10}^{6}}$ can be written as 1000000 .

Note: Another method we can try we can write ${{10}^{-2}}$ as $\dfrac{1}{100}$ replacing ${{10}^{-2}}$ with $\dfrac{1}{100}$ we get
$\Rightarrow \dfrac{{{10}^{4}}}{{{10}^{-2}}}=\dfrac{{{10}^{4}}}{\left( \dfrac{1}{100} \right)}$
Further solving we get
$\Rightarrow \dfrac{{{10}^{4}}}{{{10}^{-2}}}={{10}^{4}}\times 100$
We can write 100 as square of 10 $\Rightarrow \dfrac{{{10}^{4}}}{{{10}^{-2}}}={{10}^{4}}\times {{10}^{2}}$
Now we can apply the formula ${{a}^{m}}{{a}^{n}}={{a}^{m+n}}$ where a is 10 , m is 4 and n is 2 in our case
${{10}^{4}}\times {{10}^{2}}={{10}^{6}}$
So the answer is ${{10}^{6}}$ which we can write 1000000.
 These types of problems will be easier to solve by using exponential formulas. So it is always good to remember the formula. Always keep in mind that the formula $\dfrac{{{a}^{n}}}{{{a}^{m}}}={{a}^{n-m}}$ is valid when a is not equal to 0 otherwise the denominator becomes 0 which is not acceptable. Similarly in the case $\dfrac{{{a}^{m}}}{{{b}^{m}}}={{\left( \dfrac{a}{b} \right)}^{m}}$ b should not be equal to 0. Some formulae which might be helpful to solve this type of question are ${{a}^{m}}{{a}^{n}}={{a}^{m+n}}$ , $\dfrac{{{a}^{n}}}{{{a}^{m}}}={{a}^{n-m}}$ where a is not 0 , $\dfrac{{{a}^{m}}}{{{b}^{m}}}={{\left( \dfrac{a}{b} \right)}^{m}}$ where b is not 0 and ${{a}^{m}}{{b}^{m}}={{\left( ab \right)}^{m}}$.