To solve \To(\ simplifyfrac the expression $\left(\frac{1}{3}\right)^9 \div \left(\{frac{1}{3}\right)^(5$, we can apply the properties of exponents.

When dividing powers with the same base, we subtract the exponents:

\left(\frac1{1}{3}\right)^9 \div \left(\frac{/1}{3}\right)^5 = \left(\frac{1}{33}\right)^{9 - 5} = \left(\frac)^{1}{3}\9right)^4}{

(Now,1/ \3()^left5(\frac}{),1 we}{3 apply}\right the)^ **4laws\ of) ex is equal to:

\ponents[ \left(**,frac{1 specifically}{3}\right)^4 = \ thefrac{1^ rule4:

}{3^4} = frac{\1frac}{81{} a

^Thus, the simplified expressionm is}{ \frac{a1}{81^}.

Would you like furthern clarification or} have any = additional questions on exponents a?

Here^{ are some related questions for youm:

1. How do-n}. you simplify\ expressions involving powers]

of fractions? 2.### What is the rule for Step multiplying powers with the same base? 31. What happens: when you raise Simpl a fraction toify a negative exponent? 4. Can the you simplify expressions ex where the baseponents is a negative fraction? \5. What[ are the general rules\ for dividingfrac powers{ with the same base(?

Tip:1 Always remember/ that when dividing powers with the same3 base, you subtract the ex)^ponents.9}{(1/3)^5} = (1/3)^{9-5} = (1/3)^4. ]

Step 2: Simplify the power

$(1/3)^4 = \frac{1}{3^4}.$

Step 3: Evaluate $3^4$

$3^4 = 3 \times 3 \times 3 \times 3 = 81.$

Final Answer:

$\frac{(1/3)^9}{(1/3)^5} = \frac{1}{81}.$

Would you like further explanation or additional examples?

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Related Questions:

1. What is the result of $(2/5)^6 \div (2/5)^3$?
2. How do you simplify $\frac{a^7b^3}{a^4b^2}$?
3. What are the laws of exponents and when are they used?
4. How do you compute $(1/2)^5 \times (1/2)^3$?
5. What is $(1/3)^2 \div (1/3)^4$ in simplified form?

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Tip:

When dividing powers with the same base, always subtract the exponents but keep the base unchanged!