Question

I \[(x^2)^2\] the same as \[x^4\]

Answer 1

*Is

Answer 2

yes, because (x^2)^2 = x^(2*2)

Answer 3

\[(x^2)^2 = x^2 \times x^2 = x\times x \times x \times x = x^4 \]

Answer 4

(a^x)^x = a^(x*x)

Answer 5

x being any number of course..

Answer 6

So if i have ((x^4)/-x)^2) is it the same as x^6/-x^2

Answer 7

x^4/-x^2 = -x^(4-2)

Answer 8

\[(x^n)^m=\overbrace{\Big(\overbrace{x\times x\times x\times\dots\times x}^{\text {n times}} \big)\times\Big(\overbrace{x\times x\times x\times\dots\times x}^{\text {n times}} \big)\times\dots\times\Big(\overbrace{x\times x\times x\times\dots\times x}^{\text {n times}} \big)}^{\text{ m times}}\]

Answer 9

WHOAH

Answer 10

But is ((x^4)/-x)^2) = x^6/-x^2
if it dose the over all resolution is then
-x^6

Answer 11

\[\frac{x^n}{x^m}=\frac{\overbrace{x\times x\times x\times\dots\times x}^{\text {n times}}}{\overbrace{x\times x\times x\times\dots\times x}^{\text {m times}}}
=\frac{\overbrace{x\times x\times x}^{\text {n-m times}}\times\cancel{\dots\times x}}{{1\times\cancel{x\times x\times x\times\dots\times x}}}={x^{n-m}}{} \]

Answer 12

Is the simplified version of the -x^6?
If so then when -x^6=10^9 dose that = x=-10^3

Answer 13

i dont understand what you are saying @merh

Answer 14

Sorry, I am trying to solve this log problem and exponents just have a way with messing with my head so i am trying to clarify things.
I started with :
\[10^9=((x^2)^2/-x)^2\]
and simplified it to:
\[10^9=(x^6/-x)^2\]
and then
\[10^9=-x^6\]
and finally
\[x=10^3\]

I just wanted to make sure that this was the correct answer.

Answer 15

*\[10^9=(x^4/−x)^2\] the second time not x^6

Answer 16

ok there is a mistake

\[10^9=\left(\frac{x^4}{−x}\right)^2=\big(-x^{4-1}\big)^2=(-x^3)^2=(-x^3)\times(-x^3)=x^6\]

Answer 17

and for the final step you have to take the sixth root of both sides

\[10^9=x^6\\\sqrt[6]{10^9}=\sqrt[6]{x^6}\\10^{9/6}=x\]

Answer 18

I though that you could subtract exponents for division?
Is it not 10^3?

Answer 19

we are not dividing on this step, we are taking the sixth root

Answer 20

is the answer 10^3 yes or no?

Answer 21

nope