very hard math question, well to me?

(3^8)*(6^5)

___________

(3^10)*(6^3)

= 3^(8 - 10)*6^(5 - 3)

= 3^(-2)*6^2

= (6^2) / (3^2)

= 36 / 9

= 4

When you multiply like values you add the exponents. Similarly, when dividing, you subtract exponents.

For example, suppose you want to multiply a^5 times a^3 (the '^n' notation means 'to the power of n)

a^5 x a^3 = (a x a x a x a x a ) x (a x a x a)

= a x a x a x a x a x a x a x a

= a^8

Also a^5 divided by a^3 = (a x a x a x a x a ) / (a x a x a)

= (a x a) x (a x a x a) /(a x a x a)

= (a x a) x 1

= (a x a)

= a^2

Furthermore, since a^0 = 1 for all numbers a

1/a = a^0 / a^1

= a^(0-1)

= a^(-1)

Similarly, for any power k

1/a^k = a^(-k)

So we could have

(a x a x a x a x a ) / (a x a x a)

= a^5 x a (-3)

= a^(5-3)

= a^2

One more point: if a = mn (understood to mean m x n), then

a^k = (mn)^k = m^k x n^k

So, armed with this knowledge and knowing that 6 equals 3 x 2, your problem

3 to the 8th power times 6 to the fifth power over 3 to the 10 power times 6 to the third power

becomes

(3^8 x 6^5) / (3^10 x 6^3) = (3^8 x (3 x 2)^5) / (3^10 x (3 x 2)^3)

= (3^8 x 3^5 x 2^5) / (3^10 x 3^3 x 2^3)

= (3^(8+5) x 2^5) / (3^(10+3) x 2^3)

= (3^13 x 2^5) / (3^13 x 2^3)

= 3^13 x 2^5 x 3^(-13) x 2(-3)

= 3^(13-13) x 2^(5-3)

= 3^0 x 2^2

= 1 x 2^2

= 1 x 4

= 4

It's a bit drawn out, but it's better that you know how to solve such problems rather than simply giving you the answer.

It's not particularly difficult; it's just a matter of knowing the mechanics of operating on exponents. Once you get the idea (as demonstrated above), it will be a breeze!

Answer = 4

Use a calculator or simplify the following

(3^8 x 6^5) / (3^10 *6^3) = (3^[8-10]) x (6^[5-3]) = 3^(-2) x 6^2 = [1/3^2] x 6^2

= 1/9 x 6 x 6

= 36/9

=4

4

(3^8)(6^5)/((3^10)(6^3))

When dividing with a common base, subtract the exponents to get:

(3^(8-10)) (6^(5-3))

which simplifies to:

3^-2 * 6^2

negative exponents mean: a^-n = 1/a^n, so 3^-2=1/3^2 which is 1/9

6^2 = 36 so:

36 (1/9) =4

So the answer is 4

3^8*6^5/(3^10*6^3) =

4

____________________________

  3⁸6⁵           6⁵⁻³              6²

——– = ——– = —— = (6 ̸ 3)² = 2² = 4

 3¹⁰6³         3¹⁰⁻⁸           3²

___________________________________

(3^8 * 6^5) / (3^10 * 6^3) = 6^2 / 3^2 = 36/9 = 4

3^8 * 6^5 / 3^10 * 6^3

simplify

33333333 * 66666 / 3333333333 * 666 cancel out the 3's and 6's to get

66 / 33 or

6^2/3^2 = 36/9 = 4

(3^8 x 6^5 ) / (3^10 x 6^3) = (3^8 / 3^10) x (6^5 / 6^3) = (3^-2)(6^2) = (1 / 3^2)(6^2) = (1/9)(36) = 4