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Answer:

To simplify the expression [729^3 ÷ 729] ÷ 3^8 using the law of exponents we can break it down step by step.

First let's simplify the numerator:

729^3 = (3^6)^3 = 3^(6 × 3) = 3^18

Now let's simplify the denominator:

3^8

Next let's rewrite the expression using the simplified numerator and denominator:

[3^18 ÷ 729] ÷ 3^8

To divide exponential terms with the same base we subtract the exponents:

3^(18 - 6) ÷ 729 = 3^12 ÷ 729

To divide by 729 we can rewrite it as a power of 3:

3^(12 - 6) ÷ 3^6 = 3^6

Therefore the simplified expression is 3^6 which is equal to 729.

So [729^3 ÷ 729] ÷ 3^8 simplifies to 729.

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