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Simplify. Assume all variables are positive. (64r)^(-(2)/(3))

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Final answer:

To simplify the expression (64r)^(-(2)/(3)), we can use the negative exponent rule and evaluate the expressions in the denominator.

Step-by-step explanation:

To simplify the expression (64r)^(-(2)/(3)), we can use the exponent rules. The negative exponent means that we need to take the reciprocal of the base raised to the positive exponent. So, (64r)^(-(2)/(3)) is equal to 1/(64r)^(2/(3)).

Next, we can rewrite 1/(64r)^(2/(3)) as 1/(64^(2/(3)) * r^(2/(3))). To simplify further, we can evaluate the expressions in the denominator. 64^(2/(3)) is equal to (4^3)^(2/(3)) which simplifies to 4^2 = 16. r^(2/(3)) remains as it is.

Finally, our expression simplifies to 1/(16r^(2/(3))).

Learn more about Simplifying Exponents

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