COMPLEX FRACTION

[examman]

PLEASE HELP ME WITH THESE STEPS... 5/8 / 21/40 DO i INVERT 40/21 THEN MULTIPLY BY 5/8?

ALSO WHY DOES THE EXPONENT 4X^0 EQUAL 4 AND NOT 0?

 

[jesusfreak3]

yes to the first question. it would be (5/8) *(40/21)then simplify to (5/1) * (5/21)



the second question. 4^3 (to the third) is 4*4*4 (4 multiplied 3 times) correct? well 4 multiplied 0 times is 4.

 

[mmm4444bot]

… DO i INVERT 40/21 … NO. You invert 21/40 to OBTAIN 40/21, then continue.

(Jesus got the explanation right, but the yes-or-no response to your question is actually "No".)

… WHY DOES THE EXPONENT 4X^0 EQUAL 4 … The exponent does not equal 4. Who told you that?

The exponent in this expression is zero.

Is the caps-lock button broken on your keyboard? :?

The expression 4x^0 is a product.

It is the product of a coefficent (4) times a power (x^0).

So, Jesus did not get the explanation on this one right, although the end result is the same.

In other words, it is not that there are zero factors of 4 being multiplied together. There are zero factors of x, and that result is being multiplied by 4. (In algebra, we must always be mindful of the Order of Operations!)

The result of raising x to the zeroth power is easy to determine.

Raising any non-zero Real number x to the power of zero results in 1.

Therefore, x^0 is the same as 1 (as long as the variable x does not take on the value 0).

4 * 1 = 4

 

[Deleted member 4993]

PLEASE HELP ME WITH THESE STEPS... 5/8 / 21/40 DO i INVERT 40/21 THEN MULTIPLY BY 5/8?

What you wrote [5/8 / 21/40] - translated to fraction becomes

\(\displaystyle \frac{\frac{\frac{5}{8}}{21}}{40} \, = \, \frac{\frac{5}{168}}{40} \, = \, \frac{\frac{1}{168}}{8} \, = \, \frac{1}{1344}\)

If you wanted to write:

\(\displaystyle \frac{\frac{5}{8}}{\frac{21}{40}} \, = \frac{5}{8}\cdot \frac{40}{21}\)

then you should have written:

5/8/(21/40) or (5/8)/(21/40)

Those parentheses are very important to show the actual order of operations (PEMDAS).