Would someone be so kind to check to see if this is right please?

Simplify the expression (Simplify your answer. Use positive exponents only.)

Question

Would someone be so kind to check to see if this is right please?

Simplify the expression (Simplify your answer. Use positive exponents only.)

scarlettfarra2000 · Answer

$$\frac{ 7q ^{-1}k ^{-3} }{ w ^{0} }$$
Is the problem

scarlettfarra2000 · Answer

For every nozero number a, $$a ^{0}=1$$ using this property to rewrite the denominator 
$$\frac{ 7q ^{-1}k ^{-3} }{ 1}$$

mathstudent55 · Answer

So far, you're correct. You can simplify more since $\dfrac{a}{1} = a$ for every $a$.

scarlettfarra2000 · Answer

For every nozero number a and b integer n, $$a ^{-n}=\frac{ 1 }{ a ^{n}}$$ $$7q ^{-1}k ^{-3}=7\left(\begin{matrix}1 \ q\end{matrix}\right)k ^{-3}$$

mathstudent55 · Answer

Definition of a negative exponent:

For every nonzero $a$, 

$a^{-n} = \dfrac{1}{a^n} $

scarlettfarra2000 · Answer

Using this property $$p ^{-1}$$ and $$k ^{-3}$$$$7(\frac{ 1 }{ q }) (\frac{ 1 }{ k ^{3} })$$

mathstudent55 · Answer

Correct.

mathstudent55 · Answer

Now you have positive exponents.
You can combine the entire thing into one single fraction.

scarlettfarra2000 · Answer

$$\frac{ 7 }{ qk ^{3} }?$$

mathstudent55 · Answer

Correct.

scarlettfarra2000 · Answer

Thank you @mathstudent55

mathstudent55 · Answer

Summarizing the entire process:

$\dfrac{ 7q ^{-1}k ^{-3} }{ w ^{0} } =$

$= \dfrac{ 7q ^{-1}k ^{-3} }{ 1 }$

$= \dfrac{ 7}{q k ^{3} }$

mathstudent55 · Answer

You're welcome.
In general, a positive exponent in the numerator is a negative exponent in the denominator, and vice-versa.

mathstudent55 · Answer

Example:
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