Simplify the expression 4 over quantity of 3 x to the negative second power.

Question

mathstudent55 · Answer

Is this the porblem?
$ \dfrac{4}{(3x)^{-2} } $

anonymous · Answer

yes!

mathstudent55 · Answer

Look at the following rule of exponents:

$a ^{-n} = \dfrac{1}{a^n} $

mathstudent55 · Answer

What the rule tells you is that if you have a negative exponent, it's the same as having a positive exponent in the denominator.

Now let's use that rule of exponents for a negative exponent in the denominator to see what happens to the negative exponent.

mathstudent55 · Answer

$ \dfrac{1}{a^{-n}} $

$= \dfrac{~~~1~~~}{\dfrac{1}{a^n}} $

$= 1 \div \dfrac{1}{a^n} $

$= 1 \times a^n $

$ = a^n$

mathstudent55 · Answer

From here you see that a negative exponent in the denominator is a positive exponent in the numerator.

mathstudent55 · Answer

Now let's look at your problem.

$\dfrac{4}{(3x)^{-2} }$

$= 4 \times (3x)^{2} $

Now can you finish it?

anonymous · Answer

$$36x^{2}?$$

mathstudent55 · Answer

$= 4 \times (3x)^{2}$

$= 4 \times 9x^2$

$ = 36x^2$

You are correct. Good job!

anonymous · Answer

thank you!!