Question

Which of the following expressions are equivalent? Justify your reasoning. Please help Thank you!!

A. \[^{4\sqrt{x ^{3}}}\]
B. \[\frac{ 1 }{ x ^{-1} }\]
C.\[^{10}\sqrt{x ^{5}}\times x ^{4}\times x ^{2}\]
D. \[x ^{\frac{ 1 }{ 3 }}\times x ^{\frac{ 1 }{ 3 }}\times x ^{\frac{ 1 }{ 3 }}\]

Answer 1

@Nnesha hey you think you can help me real quick please?

Answer 2

first one is \[\huge\rm \sqrt[4]{x^3}\] ?

Answer 3

Yeah

Answer 4

alright you should know some exponent rules for that question when we multiply same bases we should `add` exponents \[\huge\rm x^m \times x^n=x^{m+n}\]
\[\huge\rm \sqrt[n]{x^m}=x^\frac{ m }{ n }\] you
can convert root to an exponent form

Answer 5

exponent if there is a negative exponent `flip` the fraction \[\huge\rm x^{-m}=\frac{ 1 }{ x^m }\]when you flip the fraction sign of the exponent would change

Answer 6

so let's do D first \[\huge\rm x^\frac{ 1 }{ 3} \times x^\frac{ 1 }{ 3 } \times x^\frac{ 1 }{ 3 }\]

Answer 7

for the first one it would be changed to

Answer 8

yes right!

Answer 9

what about B ?

Answer 10

would it be