How do you simplify $\sqrt{15 x} \cdot (21 x)$ $sqrt (15x) * (21x)$ ?

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Answer 1 · 2015-05-18T14:38:16

By exponentiial rules, we know that $a^{n} \cdot a^{m} = a^{n + m}$ $a^n*a^m=a^(n+m)$

So, in this case, if we rewrite your product:

${(15 x)}^{\frac{1}{2}} \cdot (21 x) = 15^{\frac{1}{2}} \cdot x^{\frac{1}{2}} \cdot 21 x$ $(15x)^(1/2)*(21x)=15^(1/2)*x^(1/2)*21x$

We can sum the exponentials of the variable $x$ $x$ .

$15^{\frac{1}{2}} \cdot 21 x^{\frac{3}{2}}$ $15^(1/2)*21x^(3/2)$

Simpifying more, we can even factor the constants, as both are multplied by three:

$5^{\frac{1}{2}} \cdot 3 (\frac{1}{2}) \cdot 7 \cdot 3 \cdot x^{\frac{3}{2}}$ $5^(1/2)*color(green)(3(1/2))*7*color(green)(3)*x^(3/2)$

$5^{\frac{1}{2}} \cdot 7 \cdot 3^{\frac{3}{2}} \cdot x^{\frac{3}{2}}$ $5^(1/2)*7*3^(3/2)*x^(3/2)$

Transforming all these exponentials into roots:

$7 \sqrt{5} \sqrt{{(3 x)}^{3}}$ $7sqrt(5)sqrt((3x)^3)$

How do you simplify √15x⋅(21x)sqrt (15x) * (21x)?