[w^1 / w^-3]^-4
= w3
? is this correct?
yes
See:
http://www.jiskha.com/display.cgi?id=1290294959
To simplify the expression [w^1 / w^-3]^-4, we need to apply the rules of exponents.
First, let's focus on the numerator w^1 and the denominator w^-3 separately.
In the numerator, w^1 simply means w.
In the denominator, w^-3 can be written as 1/w^3. (When a negative exponent appears in the denominator, we can move it to the numerator and change the sign of the exponent.)
Now, our expression becomes [w / (1/w^3)]^-4.
To divide by a fraction, we invert the second fraction and multiply. So we have [w * (w^3/1)]^-4.
Simplifying further, we can multiply w by w^3 to get w^4 in the numerator.
In the denominator, multiplying 1 by 1 gives 1.
Therefore, the expression becomes (w^4/1)^-4.
To remove the negative exponent, we can rewrite it as the reciprocal. So we have 1/(w^4)^4.
Finally, by applying the power of a power rule, (w^n)^m = w^(n*m), we can simplify it to 1/w^(4*4) = 1/w^16.
Hence, the correct answer is 1/w^16, not w^3.