While simplifying some math work, Peter wrote on his paper that x3 • x3 • x3 • x3 equaled x3+ 3 + 3 +3 . Did Peter simplify his work correctly and completely to a final answer? Would Peter’s work be the same if he were to simplify x3 + x3 + x3 + x3?
Simplify the given expression to rational exponent form and justify each step by identifying the properties of rational exponents used. All work must be shown.
1 over the cube root of the quantity of x to the negative 6 pwr
Simplify the given expression to radical form and justify each step by identifying the properties of rational exponents

Question

While simplifying some math work, Peter wrote on his paper that x3 • x3 • x3 • x3 equaled x3+ 3 + 3 +3 . Did Peter simplify his work correctly and completely to a final answer? Would Peter’s work be the same if he were to simplify x3 + x3 + x3 + x3? 
Simplify the given expression to rational exponent form and justify each step by identifying the properties of rational exponents used. All work must be shown.
1 over the cube root of the quantity of x to the negative 6 pwr
Simplify the given expression to radical form and justify each step by identifying the properties of rational exponents

neer2890 · Answer

x3 mean 3x or$$x ^{3}???$$

abbyrose0105 · Answer

Thanks!!

neer2890 · Answer

for what...?

abbyrose0105 · Answer

I know you didn't actually figure it out but when you wrote that it reminded me of something and I've got it now

neer2890 · Answer

okay. so what's your answer now?

abbyrose0105 · Answer

x^3 times x^3 times x^3 times x^3 = x^12 and x^3+x^3+x^3+x^3=4x^3

abbyrose0105 · Answer

I still don't have an answer to the second one though Simplify the given expression to rational exponent form and justify each step by identifying the properties of rational exponents used. All work must be shown.
1 over the cube root of the quantity of x to the negative 6 pwr

neer2890 · Answer

you mean you have to solve this$$\frac{ 1 }{ \sqrt[3]{x ^{-6}} }????$$

abbyrose0105 · Answer

yes

neer2890 · Answer

$$=\frac{ 1 }{ \sqrt[3]{\frac{ 1 }{ x ^{6} }} }=\frac{ 1 }{ \sqrt[3]{(\frac{ 1 }{ x ^{2} })^{3}} }=\frac{ 1 }{ \frac{ 1 }{ x ^{2} } }=x ^{2}$$

abbyrose0105 · Answer

How do I solve that? I want to understand it so I can do other problems similar to this

neer2890 · Answer

ok. do you know that $$x ^{-6}=\frac{ 1 }{ x ^{6} }??$$

abbyrose0105 · Answer

yes

neer2890 · Answer

and we can write $$x ^{6}=(x ^{2})^{3}$$
because we have to eliminate the cube root, that is why we have to break 6 into such power that it contains 3. and power 3 and cube root cancels with each other.

neer2890 · Answer

did you get it...?
take your time

abbyrose0105 · Answer

yes I think that makes sense

neer2890 · Answer

so,you need any other help or you can do it now....?

abbyrose0105 · Answer

is the answer x^2?

neer2890 · Answer

correct...!
good work..!