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# The expression (3a^2 b^3 c^2)^2(2a^2 b^5 c^5)^3 equals na^rb^sc^t

The expression (3a^2 b^3 c^2)^2(2a^2 b^5 c^5)^3 equals na^rb^sc^t
where n, the leading coefficient, is:

and r, the exponent of a, is:

Hi Treena,

Let us break down the expression into two parts. We will use two properties of exponents

(a*b)m = (am*bm)

and (am)n = (amn)

Using this the first one - (3a2b3c2) .

Which results in (3a2)2*(b3)2*(c2)or (32*a2*2)*(b3*2)*(c2*2) = (9*a4)*(b6)*(c4)

Therefore the first part of the expression becomes (9a4b6c4).

Now let us tackle the second part, which is (2a2b5c5)3 As before, this is equivalent to

23 * a2*3 * b5*3 *c5*3 Or, (8 * a6 * b15 * c15) = (8a6b15c15)

Putting the two parts together, we have (9a4b6c4) * (8a6b15c15)

Now we will use another property of exponents, that is, (am)*(an) = a(m + n). Using this, our expression becomes,

(9 * 8) * (a4 * a6) * (b6 * b15) * (c4 * c15) = 72 * (a10) * (b21) * (c19)

Or, 72a10b21c19 = narbsct. Comparing coefficients and exponents of like terms

Therefore, we get n = 72, r = 10, s = 21 and t = 19.

I hope this helps...