Simplify, expressing answers in terms of powers of primes?

Question

So I'm not really sure how to express these two expressions in terms of powers of primes. Help?

$16\cdot25\cdot5^2$

and

$24^5$

Using $a^m\cdot a^n=a^{m+n}, 16\cdot 25\cdot 5^2=2^4\cdot5^2\cdot5^2=2^4\cdot5^{2+2}.$ Try $24^5$ — lab bhattacharjee, Jun 15 '13 at 06:15
$16\times25\times5^2=2^4\times5^2\times5^2=2^4\times5^4$ and $24^5=(2^3\times3)^5=2^{15}\times3^5$ — , Jun 15 '13 at 06:18
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score 1 · Answer 1 · answered Jun 15 '13 at 06:20

1

Hint:

$$16=2^4$$

$$25=5^2$$

$$24=3\cdot{2^3}$$

answered Jun 15 '13 at 06:20

rurouniwallace

score 0 · Answer 2 · answered Jun 15 '13 at 06:19

0

$16 \times 25 \times 5^2 = 2^4 \times 5^2 \times 5^2 = 2^4 \times 5^{2+2} = 2^45^4$

and

2.$24^5=(8 \times 3)^5 = 8^5 \times 3^5 = (2^3)^5 \times 3^5=2^{3\times 5}\times 3^5=2^{15}3^5$

answered Jun 15 '13 at 06:19

Rusty

iostream007 · Answer 3 · 2013-06-15T06:44:44.977

0

$$16\cdot25\cdot 5^2=2^4\cdot5^2\cdot5^2=2^4\cdot5^4$$ and $$24^5=(2\cdot2\cdot2\cdot3)^5=(2^3\cdot3)^5=2^{15}\cdot3^5$$

edited Jun 15 '13 at 06:44

answered Jun 15 '13 at 06:20

iostream007

Maybe you want to replace $\Rightarrow$ with $=$? – Julian Kuelshammer Jun 15 '13 at 06:40
@JulianKuelshammer is it okay? – iostream007 Jun 15 '13 at 06:45
Looks better now. – Julian Kuelshammer Jun 15 '13 at 06:46

3 Answers3