Question

We should know that 8 = 2. To see how this is equivalent to 8% = 2 we can solve the equation 8" - 2. To

do this, we can rewrite the equation as:
(2")" = 2
How can we now use this equation to see that 8 1/3=2

Answer 1

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Answer 2

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Answer:

• show n = 1/3
• rewrite (2^3)^n as 8^(1/3)

Explanation:

By the rules of exponents, ...

(a^b)^c = a^(bc)

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(2^3)^n = 2^1 . . . . . given

2^(3n) = 2^1 . . . . . . rule of exponents

3n = 1 . . . . . . . . . . . equate exponents

n = 1/3 . . . . . . . . . . divide by 3

Recognize that 2^3 = 8, and 2^1 = 2, then substitute into the given equation:

8^(1/3) = 2