### Video Transcript

Make π‘ the subject of the formula
π equals the cube root of five over π‘ squared plus four.

So the key thing about this
question is that π‘ is what weβre trying to make the subject of the formula. Okay, so weβve got π is equal to
the cube root of five over π‘ squared plus four. So therefore, the first step is to
actually subtract four from each side. So we get π minus four is equal to
the cube root of five over π‘ 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 π‘
squared. And to actually enable us to do
that, what weβre gonna do is actually cube both sides of our equation, which is
gonna give us π minus four all cubed is equal to five over π‘ squared.

And then, what weβre gonna do is
actually multiply each side of the equation by π‘ squared cause we actually got that
down as the denominator. We donβt want it as a
denominator. So weβre gonna multiply each side
by π‘ squared. So we get π‘ squared multiplied by
π minus four all cubed equals five.

Then, at this stage, we remind
ourselves that itβs π‘ that we want as the subject to the formula. So what weβre actually gonna do is
divide through by π minus four all cubed. So weβre gonna have π‘ squared is
equal to five over π minus four all cubed. So now, as weβre looking for single
π‘ as a subject to the formula, what weβre gonna do is actually square root each
side because itβs the inverse of squared because we have π‘ squared.

So now, for this next step, what
weβre actually gonna do is use a little rule we know. And thatβs the root of π over π
is actually equal to the root of π divided by the root of π. So using this rule, weβre gonna get
π‘ is equal to root five over root and then π minus four all cubed.

So now, what weβre gonna do is
actually use one of our index rules to actually simplify this further because we
know that the πth root of π₯ is equal to one over π. So therefore, we can actually
rewrite this as π‘ is equal to root five over and then weβve got π 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 π₯ to
the power of π to the power of π is equal to π₯ to the power of ππ. So we actually multiply the
powers. So therefore, we can say that if we
make π‘ the subject to the formula π equals the cube root of five over π‘ squared
plus four, we get π‘ equals root five over π minus four to the power of three over
two.

And we got that last bit because we
had π 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.