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Question
evaluate 8^-5/3
Hi Toi,
Do you mean 8^(-5/3) with the whole "-5/3" in the exponent?
We can view 8 as 2^3 because 8=2*2*2.
So, 8^(-5/3) = (2^3)^(-5/3)
Note: When written by hand, both exponents "3" and "-5/3" are written as superscripts at the same level with the same vertical offset.
Quick review of index laws:
First, (x^a)^b = x^(a*b).
Second,(x^a)*(x^b) = x^(a+b).
The first rule is the relevant one here. Thus,
8^(-5/3)
= (2^3)^(-5/3)
= 2^(3*-5/3) ...obviously, the "3" in the numerator cancels with the "3" in the denominator
= 2^(-5)
= 1/(2^5)
= 1/32
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Josh
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When I work through problems, I like to emphasize concepts which I believe are worth noting. I will try to answer questions in the following areas, but not at the advanced level. Algebra. Sequences & Series. Trigonometry. Functions & Graphs. Coordinate Geometry. Quadratic Polynomials. Exponential & Logarithms. Basic Calculus. Probability, Permutation and Combination. Mathematical Induction. Complex numbers. Physics problems.
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