Without a calculator, you should approach this kind of exponent part by part.
Negative exponent just means the exponent of the base's reciprocal. For example, (5/6)^(-3) would be (6/5)^(3).
Also, the denominator part of the exponent represents the root of the base, and you can calculate the numerator part of the exponent as if you are calculating a simple exponent. For example, (4)^(3/2) would be (square root of 4)^(3), which is 2^3=8.
Back to the question, we can change the negative exponent to a positive exponent by changing the base to its reciprocal. So the first step would be (0.125)^(-2/3) = (8)^(2/3). Next, we can solve the denominator part of the exponent, which would be (cube root of 8)^2, which is 2^2. As 2^2 would just be 4, 4 would be the final answer.
this made sense, thank you so much
Hi, thank you for your question.
Without a calculator, you should approach this kind of exponent part by part.
Negative exponent just means the exponent of the base's reciprocal. For example, (5/6)^(-3) would be (6/5)^(3).
Also, the denominator part of the exponent represents the root of the base, and you can calculate the numerator part of the exponent as if you are calculating a simple exponent. For example, (4)^(3/2) would be (square root of 4)^(3), which is 2^3=8.
Back to the question, we can change the negative exponent to a positive exponent by changing the base to its reciprocal. So the first step would be (0.125)^(-2/3) = (8)^(2/3). Next, we can solve the denominator part of the exponent, which would be (cube root of 8)^2, which is 2^2. As 2^2 would just be 4, 4 would be the final answer.
Does this answer your question?