Chapter B, Problem 1P

Simplify each quotient.

$\frac{y^{10}}{y^6}$

To determine

To simplify:

The quotient $\frac{y^{10}}{y^6}$.

Answer to Problem 1P

Solution:

$\frac{y^{10}}{y^6}=y^4$

Explanation of Solution

Definition:

Quotient rule for exponents:

If $m$ and $n$ are positive integers, and $a$ is a real number, then

$\frac{a^m}{a^n}=a^{m-n}$

and $a$ is not zero.

Calculation:

Given quotient:

$\frac{y^{10}}{y^6}$

Using the quotient rule, we get

$\frac{y^{10}}{y^6}=y^{10-6}$

$=y^4$

Thus, $\frac{y^{10}}{y^6}=y^4$.

Final statement:

Therefore, the quotient $\frac{y^{10}}{y^6}=y^4$.