Question

Simplify. Assume that no variable equals 0. $$ \left(n^{3}\right)^{3}\left(n^{-3}\right)^{3} $$

   Simplify. Assume that no variable equals 0.
$$
\left(n^{3}\right)^{3}\left(n^{-3}\right)^{3}
$$

Algebra 2

Holliday, Luchin,… 1st Edition

Chapter 6, Problem 7

Instant Answer

Solved by Expert Ashley High

03/03/2020

Step 1

So, we have: $$ \left(n^{3}\right)^{3}\left(n^{-3}\right)^{3} = n^{3 \times 3} \cdot n^{-3 \times 3} = n^{9} \cdot n^{-9} $$ Show more…

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Simplify. Assume that no variable equals 0. $$ \left(n^{3}\right)^{3}\left(n^{-3}\right)^{3} $$

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Key Concepts

Power of a Power Rule

This rule states that when raising an exponent to another exponent, you multiply the exponents. For example, (a^b)^c becomes a^(b*c). This allows the expression to be simplified in a stepwise manner by reducing nested exponents.

Multiplication Rule for Exponents

When multiplying terms with the same base, you add their exponents. In general, a^b * a^c equals a^(b+c). This is crucial for combining terms that have been individually simplified using the power of a power rule.

Negative Exponent Rule

A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. Specifically, a^(-b) is equivalent to 1/(a^b), which is a key idea when simplifying expressions that contain negative exponents.

Zero Exponent Rule

Any non-zero base raised to the power of 0 is equal to 1. This property is used to simplify expressions when the sum of exponents results in zero, effectively reducing the expression to 1.

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