# Video: Pack 2 • Paper 1 • Question 15

Pack 2 • Paper 1 • Question 15

02:37

### Video Transcript

Make 𝑡 the subject of the formula 𝑠 equals the cube root of five over 𝑡 squared plus four.

So the key thing about this question is that 𝑡 is what we’re trying to make the subject of the formula. Okay, so we’ve got 𝑠 is equal to the cube root of five over 𝑡 squared plus four. So therefore, the first step is to actually subtract four from each side. So we get 𝑠 minus four is equal to the cube root of five over 𝑡 squared.

Then, next, what we actually want to do is the inverse of the cube root because we got the cube root of five over 𝑡 squared. And to actually enable us to do that, what we’re gonna do is actually cube both sides of our equation, which is gonna give us 𝑠 minus four all cubed is equal to five over 𝑡 squared.

And then, what we’re gonna do is actually multiply each side of the equation by 𝑡 squared cause we actually got that down as the denominator. We don’t want it as a denominator. So we’re gonna multiply each side by 𝑡 squared. So we get 𝑡 squared multiplied by 𝑠 minus four all cubed equals five.

Then, at this stage, we remind ourselves that it’s 𝑡 that we want as the subject to the formula. So what we’re actually gonna do is divide through by 𝑠 minus four all cubed. So we’re gonna have 𝑡 squared is equal to five over 𝑠 minus four all cubed. So now, as we’re looking for single 𝑡 as a subject to the formula, what we’re gonna do is actually square root each side because it’s the inverse of squared because we have 𝑡 squared.

So now, for this next step, what we’re actually gonna do is use a little rule we know. And that’s the root of 𝑎 over 𝑏 is actually equal to the root of 𝑎 divided by the root of 𝑏. So using this rule, we’re gonna get 𝑡 is equal to root five over root and then 𝑠 minus four all cubed.

So now, what we’re gonna do is actually use one of our index rules to actually simplify this further because we know that the 𝑎th root of 𝑥 is equal to one over 𝑎. So therefore, we can actually rewrite this as 𝑡 is equal to root five over and then we’ve got 𝑠 minus four to the power of three then this all to the power of a half.

And then, we can actually use one more index law to just help us get to our final solution. And that index law is that 𝑥 to the power of 𝑎 to the power of 𝑏 is equal to 𝑥 to the power of 𝑎𝑏. So we actually multiply the powers. So therefore, we can say that if we make 𝑡 the subject to the formula 𝑠 equals the cube root of five over 𝑡 squared plus four, we get 𝑡 equals root five over 𝑠 minus four to the power of three over two.

And we got that last bit because we had 𝑠 minus four to the power of three to the power of a half. Then, we actually used the index law, multiplied them together. And three multiplied by a half gives us three over two.