Simplify 81 over four multiplied by negative two over three squared multiplied by the root of one over nine.
So, first of all, what we want to do if we want to solve this problem and simplify is deal with each of our terms individually. So, the first term we’re gonna have a look at is negative two over three squared. So, to simplify this term, what we’re gonna do first of all is to use a relation that we know. And that’s if we have 𝑎 over 𝑏 all squared, this is equal to 𝑎 squared over 𝑏 squared. So therefore, we’re gonna have negative two squared over three squared. So therefore, we can say that negative two over three all squared is gonna be equal to four divided by nine or four-ninths. And this is because if we square negative two, we get four. That’s cause a negative multiplied by a negative is a positive. And if we square three, we get nine.
Well, then, next we’ve got root one over nine. Well, we can use another relationship we know to help us with this. And that’s if we have root 𝑎 over 𝑏, it’s equal to root 𝑎 divided by root 𝑏. So therefore, we’re gonna get root one over nine is equal to root one over root nine. And this is gonna give us the answer one over three. And that’s cause root one is just one. And root nine is three.
So great, we’ve now simplified both these terms. So, we can put the whole expression back together. And when we do that, we get 81 over four multiplied by four over nine multiplied by one over three. So now, if you wanna simplify this, what you’d usually do with the multiplication with fractions is multiply the numerators and denominators. However, this will give us quite large numbers and it might be quite unwieldy to deal with. So, is there an easier way of simplifying? Well, yes because we can cross cancel.
So, the first thing we can cross cancel are the fours because we can see that we’ve got four and four. We’ve got four on a denominator and four on a numerator. Well then, what we can do is we can cancel the nine as the denominator. And that’s because we’ve got 81 and nine, and if we divide 81 by nine, we get nine. So then, we’re left with nine over three. That’s cause we’ve got nine multiplied by one, which is nine, and then over three which gives us our final answer of three. So therefore, we can say that if we simplify 81 over four multiplied by negative two over three squared multiplied by the root of one over nine, the answer is three.