Bunuel wrote:
It's given there as a general rule, so yes, it's ALWAYS true.
\((-2^3)^2 = (-8)^2 = 64\).Or since 2 is even, then \((-2^3)^2 = (2^3)^2=8^2=64\).
Or \((-2^3)^2 = (-1*2^3)^2 = (-1)^2*2^6 = 64\).
As I explained
here the minus sign just means "multiplied by -1" and the exponent of 2 should be applied to -1 too.
If it were \(-((2^3)^2)\), then \(-((2^3)^2)=-(2^6)=-64\).
Hi
Bunuel - I agree on the yellow.
However when I do these exponent questions - -- I do it this way instead
I tend to multiply the exponents first (that way, there are fewer exponents) Example - \((+2^3)^2 \) ------> \( +2^6 \) --------> +64
I am most comfortable doing the above strategy
But when the
base is negative, my strategy of
multiplying exponents first FAILS
\((-2^3)^2\) -------> \( -2^ 6\) ------------>
-64I know
-64 is wrong
I am struggling to see, what is the LOGIC BEHIND why my strategy of multiplying exponents first, fails when the base of the exponent itself is negative
Thank you !
I'll try one last time.
Here: \(((-2)^3)^2\) we can say that the base is -2. Then \(((-2)^3)^2 =(-2)^6=64\).
Here: \((-2^4)^2\), as explained above, -2^4 means -1*2^4 and power of 2 should be applied to both -1 and 2^4: \((-2^4)^2=(-1)^2*2^8=2^8\).
I hope you understand the difference between -2^4 and (-2)^4. The base in the first case is 2, NOT -2, while the base in the second case is -2.