Alg 2 Question?

Question

How do I evaluate the following two expressions. Write your answer without exponents.

(1 / 8) ^ -4/3 =

125 ^ -2/3 =

Thanks so much for your help

Answer 1

Let's simplify first:

if you have a exponent, you should multiply the number as many as the exponent

2^3 = 2 * 2* 2

if you have a fractional exponent, you should multiply the number as many as the nominator and take the root of denominator

8^(2/3) = cubic root ( 8 * 8 ) = 4

if you have a negative exponent, it's 1 over multiplication the number as many as the exponent

3^(-4) = 1 / (3 * 3 * 3 * 3)

Now we can solve:

(1 / 8) ^ -4/3 = 8 ^ (4/3) = 2 ^ 4 = 16

125 ^ (-2/3) = 5 ^ (-2) = 25 ^ (-1) = 1/25

Answer 2

Question 1
= 8^(4/3)
= 2^4
= 16

Question 2
= 1 / (125)^(2/3)
= 1 / 5²
= 1 / 25

Answer 3

The thing you need to know here is that when you have anything to the power of a negative its the inverse to the power... e.g. 8^-2 = 1/(8^2) = 1/64

using that its easier to solve

(1 / 8) ^ -4/3
= 1/(1/8)^4/3
= 8^4/3
= 2^4
= 16

125 ^ -2/3
= 1/125^2/3
= 1/5^2
= 1/25

Hope that helps ^_^

Answer 4

I'll answer it this way:

if you see a value to a negative power, it means 1 over the equation. the denominator in the power is the root power

x^(1/3) is the cube root of x,
x^(-1/3) is one over the cube root of x

prime factor the number 8
8 = 2 * 2 * 2
(1/8) = (1/2)(1/2)(1/2)
since it is negative 4, you get
(1/(1/2))^4 = 2^4 = 16

prime factor 125
5*5*5
1/5^2
1/25

Answer 5

(1 / 8) ^ -4/3 = 2^4 = 16

125 ^ -2/3 = 1/(5^2) = 1/25

Answer 6

1/8^-4/3=8^4/3=8x8^1/3=8xcubicroot 8=16

125^-2/3=(cubicroot125)^-2=5^-2=1/25

Answer 7

(1 / 8) ^ -4/3 =
= (1/2^3)^(-4/3)
= (2^-3)^(-4/3)
= 2^[(-3)(-4/3)]
= 2^4
= 16

125 ^ -2/3
= (5^3)^(-2/3)
= 5^[(3)(-2/3)]
= 5^-2
= 1/25