Question

which is the simplified form of the expression (612(%)*: (604x9%) ??012OOp 2760help i’m gonna cry this is a timed not test it’s practice and i need help <:(

Answer 1

The question to simplify is:

$(p^2q^5)^{-4}\cdot(p^{-4}q^5)^{-2}$

We can use the power property of exponents to simplify this further. The power property is >>>

$(a^n)^m=a^{nm}$

Simplifying, we get:

$\begin{gathered} (p^2q^5)^{-4}\cdot(p^{-4}q^5)^{-2} \\ p^{-8}q^{-20}\cdot p^8q^{-10} \end{gathered}$

When we have two same bases multiplied, we add the exponents. So, let's simplify the exponents of "p" and "q":

$\begin{gathered} p^{-8}q^{-20}\cdot p^8q^{-10} \\ =p^{-8+8}q^{-20-10} \\ =p^0q^{-30} \end{gathered}$

We know anything to the power 0 is "1". So, we have:

$\begin{gathered} p^0q^{-30} \\ =1\cdot q^{-30} \\ =q^{-30} \end{gathered}$

To make the exponent positive, we take the variable to the denominator, so it becomes >>>

$\begin{gathered} q^{-30} \\ =\frac{1}{q^{30}} \end{gathered}$

**The first answer choice is right**