Simplify and explain- 102-15322- 3 -55-64

10^2×15^32^2× 3×5^5×6^4 =(2× 5)^2×(3× 5)^32^2× 3×5^5×(2× 3)^4 =2^2×5^2×3^3×5^32^2× 3×5^5×2^4×3^4 =2^2×3^3×5^2+32^2+4×3^1+4×5^5 =2^2×3^3 ...

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Byju's Answer

Standard VIII

Mathematics

Exponents with like Bases

Simplify and ...

Question

Simplify and explain:-
$\frac{10^{2} \times 15^{3}}{2^{2} \times 3 \times 5^{5} \times 6^{4}}$

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Solution

$\frac{10^{2} \times 15^{3}}{2^{2} \times 3 \times 5^{5} \times 6^{4}}$
$= \frac{{(2 \times 5)}^{2} \times {(3 \times 5)}^{3}}{2^{2} \times 3 \times 5^{5} \times {(2 \times 3)}^{4}}$
$= \frac{2^{2} \times 5^{2} \times 3^{3} \times 5^{3}}{2^{2} \times 3 \times 5^{5} \times 2^{4} \times 3^{4}}$
$= \frac{2^{2} \times 3^{3} \times 5^{2 + 3}}{2^{2 + 4} \times 3^{1 + 4} \times 5^{5}}$
$= \frac{2^{2} \times 3^{3} \times 5^{5}}{2^{6} \times 3^{5} \times 5^{5}}$
$= 2^{2 - 6} \times 3^{3 - 5} \times 5^{5 - 5}$
$= 2^{- 4} \times 3^{- 2} \times 5^{0}$
$= \frac{1}{16} \times \frac{1}{9} = \frac{1}{144}$

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Simplify and explain:-102×15322×3×55×64

102×15322×3×55×64=(2×5)2×(3×5)322×3×55×(2×3)4=22×52×33×5322×3×55×24×34=22×33×52+322+4×31+4×55=22×33×5526×35×55=22−6×33−5×55−5=2−4×3−2×50=116×19=1144

Simplify and explain:-
$\frac{10^{2} \times 15^{3}}{2^{2} \times 3 \times 5^{5} \times 6^{4}}$