Question

16^3 = 4^x

Answer 1

\(\bf 16^3 = 4^x\qquad \color{blue}{16=4^2}\\ \quad \\
16^3 = 4^x\implies (4^2)^3=4^x\)

so... what do you think?

Answer 2

im very confused when it comes to math. Do you think you could explain it to me in parts. if you have the time.. :/

Answer 3

well... do you know your exponent rules? like say what's \(\bf (a^n)^m=\square ?\)

Answer 4

not really.

Answer 5

http://www.onlinemathlearning.com/image-files/ari121.gif <--- 3rd rule there

Answer 6

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

Answer 7

okay im following so far.

Answer 8

\(\bf 16^3 = 4^x\qquad 16=4^2\\ \quad \\
16^3 = 4^x\implies (4^2)^3=4^x\implies \large 4^{\color{red}{2\cdot 3}}=4^\color{red}{x}\)

Answer 9

so... what do you think is "x"?

Answer 10

im stareing and im reading it over and over. and its not clicking in my head.

Answer 11

is x 23?

Answer 12

x23?

Answer 13

6 maybe? lol My brain is stuck!! errrgg!

Answer 14

\(\begin{array}{llll}
\large 4^{2\cdot 3}&=\large 4^x\\
&\uparrow \\
&\textit{if this is to be EQUALS}\\
&\textit{then both expressions must equal each other}\\
&\textit{the bases as well as their exponents}
\end{array} \)

Answer 15

yes... thus 2*3 = x :)

Answer 16

\(\large\bf 4^{2\cdot 3}=4^{x\implies 2\cdot 3\implies 6}\)

Answer 17

hmm

Answer 18

an example.. say if we make their exponent different, let's see what we get \(\large \begin{array}{llll}
4^2\ne4^5\\
4^9\ne 4^3\\
4^{15}\ne 4^{27}\\
4^{13}\ne 4^8
\end{array}\)

so you see, if the exponents differ, on the bases which are the same, you'd lose the equality of the EQUATION
the only way for the equation to be true, is if both exponents are equal