Simplify the expression completely. Write your answer only using positive exponents. (2a^0bc^-3)^-3/a^-5bc*2a^2b^0c^4

Answer 1

Hi Sandy!

There are a variety of ways to apply exponent properties here, but as long as you do so correctly, all roads should lead to the same simplified term. You can start by using the power of a power property in the numerator, although this also involves the negative exponent property. So, 2 to the -3 power is 1/8, meaning that coefficient of 8 will move to the denominator. Meanwhile, you multiply exponents for the variables, meaning you still have a^0 in the numerator along with b^-3 and c^9.

Meanwhile, you can apply the power property in the denominator. Since there is a coefficient of 2, that gets multiplied by the 8 that we just dropped to the denominator, while we add the exponents for the rest of the variables when the base is the same. a^-5 and a^2 give us a^-3, b and b^0 give us b^1 (or just b), while c and c^4 give us c^5.

In short, your new expression is:

[a^0 b^-3 c^9] / [16 a^-3 b^1 c^5]

Now, we can use the quotient property to subtract numerator exponents by denominator exponents where the bases are the same, and we end up with:

[a^3 b^-4 c^4] / 16

However, we don't want any negative exponents in our final term, so we move the b^-4 to the denominator to make the exponent positive, and our final simplified term is:

[a^3 c^4] / [16 b^4]

I hope this is helpful, and please send along any questions if you have them.

Thanks and best,

Zach

Answer 2

(2a^0bc^-3)^-3/a^-5bc*2a^2b^0c^4

a⁰ and b⁰ =1

have expression=((2bc^-3)^-3)/(a^-5bc*2a²c⁴)

same as (2^-3b^-3c⁹)/(2a^-3bc⁵)=a³c⁴/16b⁴