MHB Divide Fractions: Is Subtraction of Exponents Correct?

[DawnC]

When you divide a fraction, you minus the exponent - correct?

Example: x^9/x^4 you take the 9-5 = 5 so it would be x^5 -correc?

 

[MarkFL]

Yes, one of the rules of exponents is:

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

Thus, we find:

$$\frac{x^9}{x^4}=x^{9-4}=x^5$$

Another way to look at this is to write:

$$\frac{x^9}{x^4}=\frac{x^5\cdot x^4}{x^4}=\frac{x^5\cdot\cancel{x^4}}{\cancel{x^4}}=x^5$$

This relies on another rule of exponents:

$$a^b\cdot a^c=a^{b+c}$$

 

[phymat]

When you divide a fraction, you minus the exponent - correct?

Divide a fraction? Dividing a fraction means something like this : $\displaystyle\frac{\frac{a}{b}}{c}$ .
What you want to say is : When you solve an exponential fraction, you subtract the exponents - correct?
Yes, correct, but only when the bases are same.
We subtract the exponent of the denominator from the exponent of the numerator.
$\displaystyle\frac{a^m}{a^n}=a^{m-n}$