Question

.

Answer 1

Looks like Blake was right. Let me look at the other ones and I will give you the steps

Answer 2

Eloise is also correct. Now for the explanations...

Answer 3

In Blake's case looking at the numerator you have variables with the same base (x) so you can add the exponents together. The exponents, however, are a fraction and need to have the same denominator. They do so 4/3 + 7/3 = 11/3.

We have \[\frac{x ^{\frac{ 11 }{ 3 }} }{x ^{\frac{ 2 }{ 3 }}}\]

When a fraction is in the denominator you can bring it to the numerator by adding a minus to the exponent. So, we have:

\[x ^{\frac{ 11 }{ 3 }} * x ^{\frac{ -2 }{ 3 }}\]
By the same process explained above, we add these and get:

\[x ^{9/3}\]

aka: x^3

Answer 4

Zoe's case you add exponents and get \[\sqrt[5]{x ^{15}}\]
which is the same as\[x ^{\frac{ 15 }{ 5 }}\]

aka x^3

Answer 5

Eloise has the same kinda thing... simplifies to \[x ^{\frac{ 21 }{ 7 }}\]

aka x^3

Answer 6

Dylan is wrong however...

adding up the exponents gives \[x ^{\frac{ 7 }{ 3 }}\] and \[\sqrt[3]{x}\] can be rewritten as \[x ^{\frac{ 1 }{ 3 }}\]

so he comes out with \[x ^{\frac{ 8 }{ 3 }}\]

not x^3

Answer 7

they are all right except for Dylan

Answer 8

sorry the equations are kinda small idk how to make bigger and no problem.

Answer 9

Depends how challenging they are haha. I also have to work on my own homework pretty soon, but I could try a couple.