How do you simplify #3 sqrt x^15#?

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Answer 1 · 2016-03-03T23:21:50

#3x^"15/2"#

Recall that a square root is the same as a #"1/2"# power.

Thus,

#3sqrt(x^15)=3(x^15)^"1/2"#

Now, use the rule:

#(a^b)^c=a^(bc)#

Multiply #15# and #"1/2"#:

#=3x^"15/2"#

Answer 2 · 2016-03-03T23:31:57

#3x^7sqrtx#

Try to rewrite #x^15# in terms of squared terms.

#x^15=x^14 * x=(x^7)^2 * x#

Thus, we have

#3sqrt(x^15)=3sqrt((x^7)^2 * x)#

The #(x^7)^2# term can be brought out of the square root term without the squared part.

#=3x^7sqrtx#