Simplify (1/3^5)^5?

Question

Simplify (1/3^5)^5?

Answer

Answer

Multiply rot 5 by root five and your answer will come 1/3^25. Then to write it in standard form write as 3^-25

Answer

Simplifying the expression (1/3^5)^5 involves evaluating the exponentiation and simplifying the resulting fraction. Let's break down the steps to simplify the expression:

Step 1: Evaluate the exponentiation
To evaluate the exponentiation, we need to raise the base (1/3^5) to the power of 5. This can be done by multiplying the exponent of the base by the exponent outside the parentheses:

(1/3^5)^5 = 1/3^(5*5)

Simplifying further:

(1/3^5)^5 = 1/3^25

Step 2: Simplify the fraction
To simplify the fraction, we need to express the denominator as a power of 3. Since 25 is not a power of 3, we can rewrite the expression in terms of a power of 3:

(1/3^5)^5 = 1/3^25 = 1/(3^3)^8

Using the exponentiation rule, we can rewrite 3^3 as (3^1)^3:

(1/3^5)^5 = 1/(3^3)^8 = 1/(3^1)^3^8

Now, using the exponentiation rule for a power of a power, we can multiply the exponents:

(1/3^5)^5 = 1/(3^1)^3^8 = 1/3^(1*3*8)

Simplifying further:

(1/3^5)^5 = 1/3^(1*3*8) = 1/3^24

Step 3: Final Simplification
The expression 1/3^24 cannot be simplified further as 24 is not a multiple of 3. Therefore, the final simplified form of (1/3^5)^5 is 1/3^24.

In summary, the expression (1/3^5)^5 simplifies to 1/3^24.

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