How do you simplify $3 {\sqrt{x}}^{15}$ $3 sqrt x^15$ ?

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Answer 1 · 2016-03-03T23:21:50

$3 x^{15/2}$ $3x^"15/2"$

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

Thus,

$3 \sqrt{x^{15}} = 3 {(x^{15})}^{1/2}$ $3sqrt(x^15)=3(x^15)^"1/2"$

Now, use the rule:

${(a^{b})}^{c} = a^{b c}$ $(a^b)^c=a^(bc)$

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

$= 3 x^{15/2}$ $=3x^"15/2"$

Answer 2 · 2016-03-03T23:31:57

$3 x^{7} \sqrt{x}$ $3x^7sqrtx$

Try to rewrite $x^{15}$ $x^15$ in terms of squared terms.

$x^{15} = x^{14} \cdot x = {(x^{7})}^{2} \cdot x$ $x^15=x^14 * x=(x^7)^2 * x$

Thus, we have

$3 \sqrt{x^{15}} = 3 \sqrt{{(x^{7})}^{2} \cdot x}$ $3sqrt(x^15)=3sqrt((x^7)^2 * x)$

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

$= 3 x^{7} \sqrt{x}$ $=3x^7sqrtx$

How do you simplify 3 sqrt x^153√x153 sqrt x^15?