Question

Can someone please help me understand how this equation is being simplified?

Answer 1

I don't understand what they are doing in each step :/

Answer 2

@thesecret20111

http://www.mathsisfun.com/algebra/exponent-laws.html

Check out the portion on "Law of Exponents"

Answer 3

First step: \(4=2\times2\), \(49=7\times7\), and \(14=2\times7\).

Second step: \(2\times2=2^2\) and \(7\times7=7^2\).

Third step: \(\left(a^b\right)^n=a^{bn}\), a property of exponents. So, you have \(\left(2^2\right)^n=2^{2n}\), and the same applies to \(\left(7^2\right)^n\).

Fourth step: \(\dfrac{a^b}{a^c}=a^{b-c}\), another property of exponents. So, \(\large\dfrac{2^{2n}}{2^{n+2}}=2^{2n-(n+2)}=2^{2n-n-2}=2^{n-2}\)

Additionally, \(a^b\times a^c=a^{b+c}\), yet another property of exponents. That's how all the 7-bases are combined.

Answer 4

Thank that clarifies a lot :)

Answer 5

You're welcome