Can you simplify these expressions involving rational exponents?

Question

#1. 512 to the 1/3 power

#2. (25/64) to the -1/2 power

Answer 1

#1 (512)^1/3
=(8*8*8)^1/3
=(8^3)^1/3
=8^(3*1/3)
=8^1
=8
#2 (25/64)^-1/2
=(25)^-1/2/(64)^-1/2
=(1/25^1/2)/(1/64^1/2)
=(1/5)/(1/8)
=(1/5)*8/1
=8/5
=1 3/5

Answer 2

1) 512^1/3 means the cube root of 512
which is 8. To check (8^3 means 8*8*8 which =512)

2) (25/64)^-1/2 means 1/(square root of 25/64) since you have a negative exponent.
The square root of 25 is 5 and the square root of 64 is 8. So now you 1/(5/8) When you have a fraction as a denominator, then you can invert the fraction ie the denominator becomes the numerator and the denominator becomes the numerator.
So 1/(5/8) = 8/5 simplified to 1.6 or 1 and 3/5. Hope this helps.

Answer 3

1. (512)^(1/3) = 8 because 8^3 =512
2. (25/64)^-(1/2)
for this you flip (25/64) to (64/25) because of the negative in the exponent so we have (64/25)^(1/2) = 8/5

Answer 4

512 to the 1/3 power is the same as doin the cube root of 512
which is 8
because the sqaure root of 512=64
25/64 to the 1/2 power is the same as the sqaure root of 64 divided by the sqaure root of 25 = 8/5

Answer 5

Question 1
512^(1/3) = 8
Check
8³ = 512

Question 2
(25/64)^(1/2) = 5/8
Check
(5/8)² = 25/64

Answer 6

512 can be written as 8*8*8 so cube root of it would be =8
25 can be written as 5*5 and 64 as 8*8 so square root of the whole expresion would be 5/8

Answer 7

You are a stupid person

#1 8

#2 5/8