Question

Simplify (125)³×(25)⁶/5¹²×(625)²

Answer 1

$\huge\boxed{\underline{\underline{\green{\tt Solution}}}} </p><p>$

$(125)³× \frac{(25)⁶}{ {5}^{12} } ×(625)²$

$= ( {5}^{3} )³× \frac{( {5}^{2} )⁶}{ {5}^{12} } ×( {5}^{4} )²$

$= {5}^{9} \times \frac{ {5}^{12} }{ {5}^{12} } \times {5}^{8}$

$= \frac{ {5}^{(9 + 12 + 8)} }{ {5}^{12} }$

$= \frac{ {5}^{29} }{ {5}^{12} }$

$= {5}^{(29 - 12)}$

$= {5}^{17}$

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Answer 2

Answer:

125 = 5^3 , 25 = 5^2, 625 = 5^4

(5^3)^3 * (5^2)^2/5^12 * (5^4)^2

(a^m)^n = a^mn

5^9(3*3) * 5^4(2*2) / 5^12 * 5^8(4*2)

(5^9)*(5^4) / (5^12) * (5^8)

a^m * a^n = a^m+n

5^(9+4) / 5^(12+8)

5^13 / 5^20

a^m/a^n = a^m-n

5^(13-20)

=5^7

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