Question

When simplifying the negative fractional powers of (8/64)^-2/3, what is the answer?

Answer 1

4 [Yes, really]

Explanation:

(8/64)^-2/3 [Wow]

(1/8)^-2/3 [Simplify 8/64 to 1/8]]

(8^-1)^-2/3 [Reformat (1/8) to 8^-1]

8^(-1*(-2/3)) [Rule of exponents: When an exponent is raised to another exponent, multiply the exponents.]

8^(2/3) [Simplify (-1(-2/3)) to (2/3)]

64^(1/3) [8^(2/3) means square the 8 and then take the cube root]

4 [The cube root of 64 is 4 (4*4*4 = 64]

Answer 2

Answer:

4

Step by step explanation:

First, we can simplify the fraction inside the negative exponent:

(8/64)^(-2/3) = (1/8)^(2/3)

Now we can apply the negative exponent by flipping the fraction:

(1/8)^(2/3) = (8/1)^(2/3)

Finally, we can simplify by raising the numerator and denominator to the 2nd power, and then taking the cube root:

(8/1)^(2/3) = (64/1)^(1/3) = 4

Therefore, the simplified value of (8/64)^(-2/3) is 4