Math PLEASE help :S?

Question

PLEASE HELP ME WITH MY MATH I'M STUCK !!!



Explain in sentences what you must do in order to find the answer of a power with a negative exponent. Use 4^-3 and (2/3)^-5 to explain what you must do and show the extended multiplications. Give the final answer for each

Answer 1

There's a rule about exponents...
(x^a)(x^b)=x^(a+b)
Another rule says that
x^0 (that's zero) = 1... as long as a <> 0.

Using these two rules,
[x^a][x^(-a)] = x^(a-a) = a^0 = 1

But, (x)(1/x) = 1, since there's another rule, x^1=x,
(x^1)*(x^?) = x^0. What's the ?? Well, 1+?=0... so the missing value is -1 So, 1/x = x^(-1). You might say that a number raised to a negative power really means the reciprocal of the number raised to a positive exponent.

4^(-3), therefore is (1/4)^3

The same holds for
(2/3)^(-5)

Does that all make sense?

Answer 2

Let's do the math first, THEN explain in words.
First, a bit of background:
We know that x^3/x^5 means xxx/xxxxx, or 1/x^2
The laws for exponents tell us that when dividing exponents with like bases, simply subtract the
exponents. Thus, x^5-x^3= x^(5-2), =x^2. This makes
sense, because x^5/x^3=xxxxx/xxx=xx, or x^2
But what about x^3/x^5?
That's xxx/xxxxx, or 1/x^2. We should be able to use
the subtraction rule. And indeed, we can.
x^3/x^5=1/x^2, or x^-2. Explanation? 1/x^2 and x^-2
mean the same thing!

Now, let's tackle your 2 questions.
4^-3 means 1/4^3
1/4^3= 1/4x4x4, =1/64

(2/3)^-5 =1/(2/3)^5
This is 1/ (2x2x2x2x2)/(3x3x3x3x3)
=1 / 32/243
As you probably know, to divide one fraction by another, invert the bottom fraction and multiply.
We get 1/1 X 243/32, =243/32

So, I've done the extended multiplications. Now to
put our procedure into words:
"In order to evaluate a power with a negative
exponent, change the power to 1 over the power
and change the sign of the exponent to a plus."

I have a hunch this is leading up to one of the Laws for Exponents: x^-2=1/x^2. Which you now know!
Good luck to you.

Answer 3

If you have a negative exponent, such as 4^-3, rewrite it as 1/4^3. In other words, the expression with a negative exponent goes to the bottom with a positive exponent.
1/4^3= 1/(4*4*4)=1/64

(2/3)^-5 = 1 / (2/3)^5 = (3/2)^5 (note in this case 1/(2/3) became 3/2
(3/2)^5 = (3/2)(3/2)(3/2)(3/2)(3/2)=7.59 (approximately)
You could have also done it this way.
1 /(2/3)(2/3)(2/3)(2/3)(2/3) and would have gotten the same result.

Answer 4

A negative exponent means the reciprocal of the corresponding positive exponent.
Thus 4^-3 = 1/4^3 = 1/64 (you can calculate the rest yourself!)

(2/3)^-5 = (3/2)^5 = 243/32 (again I leave you to finish this off!)

Answer 5

To find a ^-b, (a .ne. 0) compute a^b and turn
the answer over.
In other words, a ^-b is the reciprocal of a^b.
So 4^-3 = 1/ 4^3 = 1/64.
(2/3)^-5 = 1/ (2/3)^5 = 1/ (32/243) = 243/32.
Hope that helps!

Answer 6

4 to the -3 power is simply 1 divided by (4 to the third power). The negative sign tells you to invert the result of the exponentiation.
2/3 to the -5 power is solved the same way;. Calculate 2/3, then raise it to the 5th power, then invert the result.

You can do the arithmetic.

Answer 7

4^-3 is equal to [1/4]^3 therefore its 1/64
As for [2/3]^-5 = [2 x 3^-1] ^-5 = [2]^-5 x [3]^5 = 7.59375