The power of a half means square root, so here’s a question that says find the value of 9 to the power of a half. That’s the same as saying find the value of square root, 9. , so square root, nine or nine to the power half is equal to three. I’m going to quickly show you that this works, so if you’ve got nine to the power of a half and you multiply it by nine to the power of a half.
When you multiply indices, you add the powers, so that will give us half plus a half, makes a whole. So we’ve got nine to the power of one which we can just write as nine! So nine to the power of a half multiplied by nine to the power of a half is equal to nine, and what number multiplied by itself makes nine that’s three three times three makes nine, so nine to the power half must be equal to three. So all you need to know is that the power of a half means square root. So there’s three questions for you to try here: pause the video give them a go and press play when you’re ready for the answers.
Okay, the first one find the value of 25 to the power of a half, so square root. 25, that’s five find the value of 100 to the power of a half that will be 10 and 64 to the power of a half. That’s eight, the power of one-third means cube root, so the cube root of 27, the number that multiplies by itself and then again to get 27 is three three times three makes nine nine times. Three makes twenty seven and again i’ll quickly? Show you how this works so twenty-seven to the power third times twenty-seven to the power third times 27 to the power? third. So when we multiply, we add the indices. So a third plus a third plus a third makes one whole so 27 to have a third times 27 to the power of the third times 27 to the power of a third makes 27 and what number multiplied by itself and then again makes 27 that’s three times three times three. So 27 to the power.
Third must be equal to three. So again, what you need to know is the power of a third means, cube root. So three questions for you to try pause the video give them a go and press play when you’re ready for the answers? Okay, so 64 to the power of a third cube root, 64 is 4 4 times, 4 is 16. Sixteen times four is sixty-four. Eight to the power of one-third is two two times two makes four four times two makes eight and cube root. One two five 125 is five five times.
Five is twenty five twenty five times. Five is a hundred and twenty five okay, here’s a different question this time.
There’s two parts to it really find the value of eight to the power of two thirds? So we’ve got a three on the bottom, which means cube, root and there’s a 2 on the top, which means square! So in this question, we’re going to cube, root, 8 and then square the answer, or we could square first and cube root the answer, but usually it’s easier to do the root first.
So if we cube root 8, the cube root of eight is two, so eight to the power of two thirds is the same as two squared and we square two two times two is four? So eight to the power of two thirds is equal to four, so we had to square and cube root. So three questions for you to try here, pause the video give them a go and press play when you’re ready for the answers.
Okay, the first one 9 to the power of 3 over 2! So this time we’ve got a square root. We’ve got a square root and we’ve got to cube it. So if we square root, first do the root. First, so ninth have three over t? The square root of nine is three, so we’ve got the same as three cubed and three cubed three times three times: three: twenty, seven: okay, sixty-four to the power of two-thirds, so we’ve got our cube root and square 64.
Cubed rooted is 4, so we’ve got 4 squared and 4 squared is 16. And finally 25 to the power of 3 over 2, so we’re going to square root and cube so square root. First, so 25 square rooted is five and five cubed five times five times. Five is a hundred and twenty-five. Here we’ve got another different type of question, so we’ve got four ninths the power of a half. So when we’ve got a fraction and we’ve got to do the whole thing to the power of a half, that’s the same as square rooting, the top and square rooting the bottom so for 4, 9 to the power of a half we square root, the top. So the square root of four is two and we square root the bottom. So the square root of nine is three. So four ninths, the power half, is two thirds three questions for you to try again pause the video give them a go and press play when you’re ready for the answers, so the first one 27 over eight to the power of a third? So we’re going to cube root the top and cube root the bottom! So the cube root of 27 is three? The cube root of eight is two, so we’ve got three over two second one 64 over nine to the power of a half, so we’re going to square root. The top and the bottom square root. 64 is eight square root of nine is three, so we’ve got eight thirds and finally 125 over 64. To the power of one third. So it’s a cube root, so cube root, the top 125 cube rooted is 5 and 64 cube rooted is 4.
, so we’ve got five over four. So this time the question says: find the value of 64 over 27 to the power of minus two thirds. So when we’ve got a negative in the power, it means find the reciprocal, and that just means flip it over so find the value of 64 over 27 to the power of minus two-thirds? So that means there’s three elements so they’re over three: that’s a cube root, so we’re going to find the cube root, the 2 on top that means square it and the minus means find the reciprocal or flip it over. So let’s do all of these things.
So if we do the cube root first, so we’ve got 64 over 27 to the power of minus two-thirds? If we find the cube root first, so the cube root of 64 is four and the cube root of 27 is three. So we’ve got four over three to the power of minus two. If we square it now so 4 squared is 16!
3 squared is 9 and we’ve still got the negative, and that just means flip it over find the reciprocal so 16 over nine to the power of minus one is nine sixteenths. So two more questions again pause. The video give them a go and press play when you’re ready to carry on okay, so 16 over 25 to the power of three over two.
So that means we’ve got to do a square root? We’ve got to cube it and we’ve got to find the reciprocal or flip it over? So i’ll write 16 over 25 to the power of minus 3 over 2, so i’m going to square root first, so square root.
16 is four square root. 25 is five, and then we’ve got the power of minus three and we’re going to cube them so four times four times. Four is sixty-four five times five times. Five is a hundred and twenty-five, and that’s to the power of minus one and we’re gonna flip it over find the reciprocal which gives us 125 over 64. . The second question, so we’ve got 125 over eight to the power of minus two thirds? So we’re going to cube root this one first so cube root.
The top 125 cube roots is 5 cube root. The bottom 8 cube rooted is 2, then we’re going to square the top and the bottom so 5 squared is 25. 2 squared is 4?
And we’ve got the minus left, so we’re going to flip it over which gives us 4 over 25! ! Okay, to finish up, we’ve got three questions here, so give these ones a go and then press play when you’re ready for the answers?
Question 1 find the value of one over 27 to the power of one-third, so this means cube root, so we’re gonna cube, root, well, cube root?
The top and the bottom cube root of one is one cube. Root of twenty-seven is three, so we’ve got one third question two? This time we’ve got a square root and a reciprocal and a flip so 49 over 81, so power minus a half is the same as if we square root them first, so square root! 49 is seven square root. 81 is nine, so seven ninths to the power of minus one and we’ll flip it over, which gives us nine sevenths and finally question three! So we’re going to cube root square and flip, so i’ve got eight over one, two, five to the power of minus two thirds. If i cube root, that’s going to give me two fifths and i’ve got the power of minus two left, i’m going to square them so 4 over 25, and now i need to flip it over 25 over 4. .