P quotient rule of exponents practice

Answer 1

To practice and understand the quotient rule of exponents, let's consider the expression:

\[ \left(\frac{a^m}{b^n}\right)^p \]

According to the quotient rule of exponents, we can simplify this expression by multiplying the exponents of the numerator and denominator with the exponent outside the parentheses.

Using the quotient rule of exponents, we can rewrite the expression as:

\[ \frac{a^{m \cdot p}}{b^{n \cdot p}} \]

So, the simplified expression is:

\[ \frac{a^{mp}}{b^{np}} \]

Let's work through an example to solidify this concept:

Example:
Simplify the expression: \(\left(\frac{3^4}{2^2}\right)^3\)

Using the quotient rule of exponents, we can rewrite this expression as:

\[\frac{3^{4 \cdot 3}}{2^{2 \cdot 3}} = \frac{3^{12}}{2^6}\]

Therefore, the simplified expression of \(\left(\frac{3^4}{2^2}\right)^3\) is \(\frac{3^{12}}{2^6}\).