Question

Exponential Rules Level 3

Answer 1

The expression to simplify is:

$\frac{(3d^3z)^{-3}}{5d^{-3}z^4}$

First, we will use the power rule of exponents to simplify the numerator. The rule is:

Simplifying, we have:

$\begin{gathered} \frac{(3d^3z)^{-3}}{5d^{-3}z^4} \\ =\frac{(3)^{-3}(d^3)^{-3}z^{-3}}{5d^{-3}z^4} \\ =\frac{\frac{1}{27}d^{-9}z^{-3}}{5d^{-3}z^4} \end{gathered}$

Now, we use another exponent rule shown below to simplify it further. The rule is:

So, we have:

$\begin{gathered} \frac{\frac{1}{27}d^{-9}z^{-3}}{5d^{-3}z^4} \\ =\frac{\frac{1}{27}^{}}{5d^{-3+9}z^{4+3}} \\ =\frac{\frac{1}{27}}{5d^6z^7} \end{gathered}$

Now, we can just simplify the constants to get our final answer:

$\begin{gathered} \frac{\frac{1}{27}}{5d^6z^7} \\ =\frac{1}{(27\times5)d^6z^7} \\ =\frac{1}{135d^6z^7} \end{gathered}$The final answer is:$\frac{1}{135d^6z^7}$