Question about Simplifying Expressions Containing Variables with Exponents

[TunaInTheBrine]

QUESTION WITH ANSWER: (2x^-4)(3x^2) = 6/x^2

MY STICKING POINT: I actually get 6x^-2, and am wondering how this equates with 6/x^2.

Is it simply that the negative exponent is getting dropped to the denominator in order to make it positive, just as you would do with any exponent? Because if that is the case, then why doesn't the integer go in the denominator with it and a 1 in the numerator?

 

[Otis]

Here is the property that deals with negative exponents:

x^(-n) = 1/x^n

In the expression 6*x^(-2), the exponentiation is x^(-2). The exponent -2 does not apply to the 6 because the Order of Operations tells us to do exponentiation before multiplication. (In other words, 6 is only a coefficient, in that expression.)

If we had (6x)^(-2), instead, then the exponent applies to both the 6 and x because the base in that exponentiation is 6x.

(6x)^(-2) = 1/(36x^2)

Cheers :cool:

 

[TunaInTheBrine]

Here is the property that deals with negative exponents:

x^(-n) = 1/x^n

In the expression 6*x^(-2), the power is x^(-2). The exponent does not apply to the 6 because the Order of Operations tells us to do exponentiation before multiplication.

If we had (6x)^(-2), instead, then the exponent applies to both the 6 and x.

(6x)^(-2) = 1/(36x^2)

Cheers :cool:

Okay, so do exponents before multiplication then, but I'm still not understanding how (2x^-4)(3x^2) can be simplified to 6/x^2

Can someone break this down for me?

 

[Otis]

Sure.

You got 6*x^(-2) -- that's good.

Now, we simplify the exponentiation part (i.e., we deal with that negative exponent), by using the property in my first reply.

6*x^(-2)

6*(1/x^2)

(6/1)*(1/x^2)

6/x^2

:cool:

 

[TunaInTheBrine]

Sure.

You got 6*x^(-2) -- that's good.

Now, we simplify that power (i.e., deal with the negative exponent), using the property in my first reply.

6*x^(-2)

6*(1/x^2)

(6/1)*(1/x^2)

6/x^2

:cool:

Excellent! Thanks!

 

[Otis]

Can you rewrite the following expression, without any negative exponents?

7 * a^(-4) * b^(3) * c^(-17)