the simplest form of 4RACE TO NEGATIVE1 MRACE TO NEGATIVE2 NRACE TO NEGATIVE3ALL OVER(2MN)RACETO NEGATIVE3
WHAT IS THE SIMPLEST FORM OF 4-1M-2N-3/(2MN)-3 IS:
Please learn to type exponents as ^2 (means to the second power)
(4^(-1)m^(-2)n^(-3)/(2mn)^(-3))
(1/4 1/m^2 1/n^3)/(1/(8m^3n^3))
(1/(4m^2n^3))/(1/(8m^3n^3))
(8m^3n^3)/(4m^2n^3) = 2m
To simplify the expression 4RACE TO NEGATIVE1 MRACE TO NEGATIVE2 NRACE TO NEGATIVE3 ALL OVER (2MN) RACE TO NEGATIVE3, we need to apply the rules of exponents.
First, let's simplify the numerator:
4 to the power of -1 is the reciprocal of 4, which is 1/4.
Similarly, multiplying by M to the power of -1 and N to the power of -2 is equivalent to taking the reciprocals of M and N raised to those powers. Therefore, we have 1/M and 1/N to the power of 2.
Now, let's simplify the denominator:
2 to the power of -3 is the reciprocal of 2 cubed, which is 1/2^3 or 1/8.
Multiplying by M and N to the power of -3 is equivalent to taking the reciprocals of M and N raised to those powers. So, we have 1/M^3 and 1/N^3.
Putting it all together, the expression simplifies to:
(1/4)(1/M)(1/N)^2 all over (1/8)(1/M^3)(1/N^3).
To simplify further, we can multiply the reciprocal in the denominator by the numerator:
(1/4)(1/M)(1/N)^2 multiplied by (8/1)(M^3/1)(N^3/1).
Simplifying further:
(1/4)(8)(M^2)(N) multiplied by (1/M)(1/N)^2(M^3)(N^3).
Finally, we can cancel out common terms:
(1/4)(8)(M^2)(N)(1/M)(1/N)^2(M^3)(N^3) = 2N(M^2)(M^3)(N^3).
Therefore, the simplified form of the expression is 2N(M^5)(N^3).