Video: Simplifying Rational Algebraic Expressions Using Laws of Exponents

Simplify (π‘₯⁴𝑦⁴ Γ— π‘₯²𝑦⁴)/(π‘₯⁴𝑦³).

02:10

Video Transcript

Simplify π‘₯ to the fourth 𝑦 to the fourth times π‘₯ squared 𝑦 to the fourth over π‘₯ to the fourth 𝑦 cubed.

Okay, where should we start here? The first thing I notice is that there’re some multiplication in the numerator that I can simplify. If I’m multiplying π‘₯ to the fourth times π‘₯ squared, then I would add those two exponents together, π‘₯ to the four plus two. I can do the same thing with the 𝑦s here. 𝑦 to the fourth times 𝑦 to the fourth would be equal to 𝑦 to the four plus four.

Okay, we can simplify a little bit more. Now we have π‘₯ to the sixth power times 𝑦 to the eighth power over π‘₯ to the fourth 𝑦 cubed. When we’re dealing with dividing exponents, there’s a few ways we can think about this. We could think about it like this. π‘₯ to the sixth power means π‘₯ multiplied together six times. And over π‘₯ to the fourth power is π‘₯ multiplied together four times. If you think about it this way, then π‘₯ over π‘₯ equals one and can be crossed out, leaving us with π‘₯ squared times 𝑦 to the eighth over 𝑦 cubed.

Another way to think of this so that you don’t have to draw it out every time is to look at the exponent in the numerator and the exponent in the denominator. Here we have eight and three. What we do is we subtract three from eight. And that will give us the value that we’re left with. If we take away three 𝑦s from the eight 𝑦s on top, we’ll be left with 𝑦 to the fifth power.

The simplified form of this fraction is π‘₯ squared times 𝑦 to the fifth.

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