how to simplify when there are 3 variables to the power involved. Fractions?

Question

(x to the power 2 y power 3)power of 4 (y power of 4)p0wer 0  z power -2 divided by (xz power 2)power3) y power -5?

Answer 1

Mae, to further expand on Karin's explanation, (x²y³)⁴ = (xxyyy)(xxyyy)(xxyyy)(xxyyy). 

 

If we put everything in order, we have xxxxxxxxyyyyyyyyyyyy, which we shorthand x⁸y¹².

 

Like Karin said, ANYTHING to the power of zero equals 1.

 

When we multiply x⁸y¹² by 1 and y⁵, the same thing applies if we expand, regroup, and do our shorthand.

 

When it comes to division, remember that anything over itself equals 1. (x⁸y¹⁷)/(x³z⁸) = (xxxxxxxxyyyyyyyyyyyyyyyyy)/(xxxzzzzzzzz). x/x then happens 3 times, so they become 1(1)(1), which basically cancels out.

 

We are left with Karin's answer after we do our shorthand with what's left.

 

 

Answer 2

if this is your problem:

[(x²y³)⁴(y⁴)⁰z^-2]/[(xz²)³y^-5]

 

powers to a power are multiplied and multiplication of similar bases you add exponents. Any number to 0 power is 1. If a number is raised to a negative exponent, you take reciprocal.

 

[x⁸y¹²1y⁵]/x³z⁶z²

 

Simplifying both numerator and denominator

(x⁸y¹⁷)/(x³z⁸)

 

division you subtract exponents so finally 

x⁵y¹⁷/z⁸