(3/5)^-3 how can i solve this?

Question

could you explain?

Answer 1

(3/5)^(-3) = 1 / (3/5)³ = 1/(27/125) = 125/27

Answer 2

You need to use two rules of exponentials:
x^(-n) = 1 / (x^n) and (a/b)^n = (a^n)/(b^n)
Thus (3/5)^(-3) = (3^-3) / (5^-3) =
(5^3) / (3^3) = 125/27
Another way of looking at this: A negative exponent in the "top" is equivalent to a positive exponent in the "bottom" and vice versa. That is how the fractoin got flipped and the negative exponents became positive.

Answer 3

Hey there!

Recall that (a/b)^-c is the same as (b/a)^c. We could use this formula to simplify the answer.

(3/5)^-3 -->
(5/3)^3 -->
5^3/3^3 -->
125/27

So the answer is 125/27.

Hope it helps!

Answer 4

The rules used are:
(a/b)^(-c) = (b/a)^c
(a/b)^c = (a^c) / (b^c)

This means:
(3/5)^(-3)
= (5/3)^3
= 5^3 / 3^3
= 125 / 27.

Answer 5

The negative exponent tells you to take the reciprocal and change the neg. to pos. .....

(5/3)^3

Then that would be the same as (5^3) / (3^3) = 125 / 27

Answer 6

(3/5)^-3 = 1/(3/5)^3 = (5/3)^3 = 125/27, nearly 5
a^-b = 1/a^b

Answer 7

(3/5)^(-3) = 1/(3/5)^3 = (5/3)^3 = 125/9

Answer 8

= (5/3)^3

exponent means multiply X times, negative exponent means divide X times ... or "just flip it over and multiply".

Answer 9

the parentheses mean do this first. so 3/5= 0.6.

then u do the exponents. positive means multiply. negative means multiply but the number will be a negative with certain exponents.

in this case it's:
-0.6 times -0.6 times -0.6= -0.216

Answer 10

one over 3/5 times one over 3/5 times one over 3/5

1
--
.6 *.6 *.6

1/21.6