Question

Simplify the following expression; express your answer as a power with a base of 5.

(244140625 x 48828125^3)^4 x 625^8
________________________________________
(9765625^4 x 15625^3 ÷ 78125^8)^6

Answer 1

Thankfully these all end in 5's or 0's so they all have 5 as a factor (probably several times over seeing how ginormous they are).

You need to reduce these FIRST before trying to type that all in. Do this by taking log\(\_5\)(put # here)

Answer 2

\[\huge log_5 (number )\]

Answer 3

This will tell you the power for each

\[\huge \log_5 (625) = 4 \]
meaning
\[\huge 5^4=625\]

Answer 4

Phew this took a bit but here you go:
\[\huge \frac{(5^{12} * (5^{11})^3)^4*(5^4)^8}{((5^{10})^4*(5^6)^3/(5^7)^8)^6} \]

You should be able to find the answer from here :-)

Just review your rule of exponents:
http://www.mathsisfun.com/algebra/exponent-laws.html

Answer 5

After simplification, you get
\[
\frac{5^{(45) 4+32}}{5^{(58-56)
6}}=\frac { 5^{212}}{5^{12}}=5^{200}
\]