Question

Which expression is the simplified form of the square root of z^7?

Answer 1

First of all , I will introduce you to a property that we are going to use here.

\(a^b \times a^c = a^{b+c}\)

Answer 2

So we are going to write : \(z^7\) as in the form of \(z^4\) ,\(z^2 \) , \(z\) .

Answer 3

Can you tell me how can we write \(z^7\) in a more simplified form.

Answer 4

im a little confused,

Answer 5

Ok! no problem.

Can I write : \(z^7 \) as \(z^{1 + 4 + 2}\) ?

Answer 6

yes

Answer 7

So as mentioned above : \(a^{b+c} = a^b \times a^c\)

Similarly : \(a^{b+c+d} = a^b \times a^c \times a^d\)

Can you now tell me what I can write : \(z^{1+2+4}\) as ?

Hint : z = a, 1 = b , 2 = c , 4 = d.

Answer 8

\[z ^{1}*z ^{2}*z ^{4}\]

Answer 9

is that right?

Answer 10

Yeah !!! Very right. So now we have :
\(\sqrt{z^7} = \sqrt{z^1 \times z^2 \times z^4}\)

Right?

Answer 11

right!!

Answer 12

so since this exponent is odd, do i subtract 1 and leave that one letter inside the radical???

Answer 13

\[\Large \sqrt{z^7} = (z^7)^{\frac{ 1 }{ 2}} = \]
\[\LARGE (z^1 z^6)^{\frac{ 1 }{ 2 }} = z^{\frac{ 1 }{2 }} z^{\frac{ 6}{ 2 }}\]
The last step is just using the fact that \[\Large (ab)^x = a^x b^x\]
Now you can simplify. Depending on your class, you may need absolute value signs on the z which will now be outside the square root.

Answer 14

can you simplify \( \sqrt{z^6} \) ?
because \( \sqrt{z^7} = \sqrt{z^6}\sqrt{z^1} \)

Answer 15

or use square root is the same as using the 1/2 exponent.... as agent posted

Answer 16

so my answer would be \[z ^{3}\sqrt{z}?\]

Answer 17

yes.

notice that if you simplify
\[ z^{\frac{6}{2}} z^{\frac{1}{2}}\]
you get
\[ z^3 z^{\frac{1}{2}}\]
which can be written as
\[ z^3 \sqrt{z} \]

Answer 18

yay i get it!! thank you all for ur help!!

Answer 19

phi will u give agent0smith a medal (: they deserve one too!