Question

Help with Simplifying?

Answer 1

What is the question?

Answer 2

\[\sqrt[x]{x^4 \times x^5 \times x^6}\]

Answer 3

How would I go about simplifying this? I am very confused on what steps to take?

Answer 4

@ranga

Answer 5

\[\Large a ^{m} \times a ^{n} = a ^{m+n}\]

Answer 6

what is the the number or letter outside the radical sign? It is too small for me to see.

Answer 7

well use the idex law from multiplication, which is add the powers

as an example

\[x^a \times x^b \times x^c = x^{a + b+c}\]

and rewrite the radical in index form

\[\sqrt{x} = x^{\frac{1}{2}}\]


and the power of a power ruleis, multiply the powers

\[(x^a)^b = x^{a \times b}\]

so your problem is really

\[(x^4 \times x^5 \times x^6)^\frac{1}{x}\]

Answer 8

@ranga it is x

Answer 9

@campbell_st Thank you sooooo much! That really helped.

Answer 10

Did you simplify it?

Answer 11

Yes I was able to come up with the answer being \[x^4\]

Answer 12

wow...

based on the question, the solution is

\[\sqrt[x]{x^4 \times x^5 \times x^6} =x^{\frac{15}{x}}\]

Answer 13

\[\Large \sqrt[x]{x ^{4} \times x ^{5} \times x ^{6}} = (x ^{4} \times x ^{5} \times x ^{6})^{\frac{ 1 }{ x }} = (x ^{4 + 5 + 6})^{\frac{ 1 }{ x }} = (x ^{15})^{\frac{ 1 }{ x }} = x ^{\frac{ 15 }{ x }}\]

Answer 14

x^(15/x)

Answer 15

oh really? okay thanks, I will go back and change my answer.