How do you multiply $(25a^2b)^3(1/5abc)^2$ ?

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Answer 1 · 2015-04-22T03:49:10

Start with the exponent rule $(x^m)^n=x^(m*n)$ .

$(25a^2b)^3(1/5abc)^2$ =

$(25^3a^6b^3)((1/5)^2a^2b^2c^2)$ =

$(15625a^6b^3)((1/25)a^2b^2c^2)$ =

Divide 15625 by 25 and use the exponent rule $(x^m)(x^n)=x^(m+n)$ .

$(15625/25)(a^(6+2))(b^(3+2))(c^2)=625a^8b^5c^2$

Answer 2 · 2015-04-22T03:58:29

We know that $color(blue)((ab)^2 = a^2 * b ^2$

Hence
$(25a^2b)^3(1/5abc)^2$

$= {25^3 * (a^2)^3 * b^3} * {(1/5)^2 * a^2 * b^2 * c^2}$

$= {(5^2)^3 * a^6 * b^3} * {(1/5)^2 * a^2 * b^2 * c^2}$

$= {5^6 * a^6 * b^3} * {(1/5)^2 * a^2 * b^2 * c^2}$

Next, we group the Constants and the Same Variables together

$= (5^6*(1/5)^2)*(a^6*a^2)*(b^3*b^2)*c^2$

$= (5^6/5^2)*(a^6*a^2)*(b^3*b^2)*c^2$

Two important laws of Exponents:

$color(green)(a^m*a^n = a^(m+n) if a!=0$
$color(green)(a^m/a^n = a^(m -n) if a!=0$

Applying these, we get

$= (5^(6-2))(a^(6+2))*(b^(3+2))*c^2$

$= 5^4 * a^8 * b^5 *c^2$

$= 625a^8b^5c^2$

How do you multiply (25a^2b)^3(1/5abc)^2(25a^2b)^3(1/5abc)^2?