Video Transcript
Find the value of 𝑦 given that
negative 1000𝑦 cubed minus 27 equals zero.
So, we’ve got with our equation,
negative 1000𝑦 cubed minus 27 equals zero. So, now what we want to do is we
want to add 27 to each side of the equation. So that way, we’ve got the negative
1000𝑦 cubed on its own on the left-hand side. And when we do that, we get
negative 1000𝑦 cubed is equal to 27. So, what’s the next step? Well, now we want the 𝑦 cubed on
its own. So, what we’re gonna have to do is
divide both sides by negative 1000. Now, if we divide both sides by
negative 1000, what we’ll get is 𝑦 cubed is equal to 27 over negative 1000.
Well, if you divide something by a
negative, it means that the result is gonna be negative. So, we can rewrite the right-hand
side as negative 27 over 1000. Okay, but that’s 𝑦 cubed. What we want to do is find 𝑦. So, what do we need to do now? Well, what we want to do is do the
inverse of cubing. So, we want to take the cube
root. So, when we do this, it’s gonna be
the same as the cube root of negative 27 over 1000.
Well, what we can do now is use one
of the relationships we know. And that is that if we have the
cube root of 𝑎 over 𝑏, that’s the same as the cube root of 𝑎 over the cube root
of 𝑏. Which means we’re gonna have 𝑦 is
equal to, and I’ve taken the negative out, so 𝑦 is equal to negative, then we’ve
got cube root of 27 over the cube root of 1000. So, what this is gonna give us is
𝑦 is equal to negative three over 10. And that’s cause we said cube root
of 27 is three, cube root of 1000 is 10. So, that means we found our value
of 𝑦.
