Question

How do you write the variable expression for the quotient of ten to the seventh power and ten?

Answer 1

Find the variable expression of ‘ten to the seventh power’ and ‘ten’ by taking them separately. For the quotient part, take the numerator as ‘ten to the seventh power’ i.e. ${{10}^{7}}$ and the denominator as ‘ten’ to get the required variable expression.

Complete step by step answer:
We can convert the given word problem to variable expression by taking each part of the word problem and forming the variable expression simultaneously.
Coming to the first part of the word problem
Ten to the seventh power$={{10}^{7}}$
For the second part, we know the numeric value of ‘ten’$=10$.
Since the quotient of these two are asked, hence we can take ‘ten to the seventh power’ in numerator and ‘ten’ in denominator.
So, the quotient of ten to the seventh power and ten$=\dfrac{{{10}^{7}}}{10}$
This is the required variable expression.

Note: In the quotient, the part which is asked first should be taken as numerator and the part asked later should be taken as denominator. So, for our question ‘ten to the seventh power’ is taken as numerator and ‘ten’ is taken as denominator. Taking the reverse would lead to expression error. Since only the expression is asked in the question we have written the solution till that only. Our expression can further be simplified as
$\dfrac{{{10}^{7}}}{10}$
As we know, $\dfrac{{{a}^{m}}}{{{a}^{n}}}={{a}^{m-n}}$
So, our expression can be written as
$=\dfrac{{{10}^{7}}}{{{10}^{1}}}={{10}^{7-1}}={{10}^{6}}$
This is the simplified form of the required expression.