2006-10-22 04:24:31 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
8^(-2/3)=1/(8^(2/3))
{positive rational exponent}
=1/4^(3/3)=1/4^(1)=1/4
2006-10-22 04:38:22 · answer #1 · answered by Anonymous · 0⤊ 0⤋
We need to remember the following rule for negative exponents:
x^(-a) = 1/x^a....In other words, any number raised to a negative exponent equals 1 divided by the same number raised to the same POSITIVE exponent.
Your question:
8 raised to the negative 2/3 becomes
1/8^(2/3)
By the way, you can break this fraction down further but you asked for a positive rational exponent and now you have it.
Guido
2006-10-22 04:33:03 · answer #2 · answered by Anonymous · 0⤊ 0⤋
8^ -2/3=8^(-2/3)
=1 / 8^ (2/3)
2006-10-22 04:34:25 · answer #3 · answered by Anonymous · 0⤊ 0⤋
a^(-x) = (a^(-1))^x = (1/a)^x, so 8^(-2/3) = (1/8)^(2/3).
2006-10-22 04:31:41 · answer #4 · answered by James L 5 · 0⤊ 0⤋
8^(-2/3)= 1/(8^(2/3))
2006-10-22 04:31:03 · answer #5 · answered by ironduke8159 7 · 0⤊ 0⤋
1/8^2/3 (as -ive always represent that no. should always turned into 1 upon it does not matter if it is in denominator or numerator)
2006-10-22 04:39:35 · answer #6 · answered by Anonymous · 0⤊ 0⤋
8^(-2/3) = 1/(8^(2/3)) = 1/((cbrt(8)^2) = 1/(2^2) = 1/4
2006-10-22 10:49:18 · answer #7 · answered by Sherman81 6 · 0⤊ 0⤋