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Write the following expression without negative exponents and without parentheses. (3x)^(-3) Answer:

Write the following expression without negative exponents and without parentheses.\newline(3x)−3 (3 x)^{-3} \newlineAnswer:

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Full solution

Q. Write the following expression without negative exponents and without parentheses.\newline(3x)−3 (3 x)^{-3} \newlineAnswer:
  1. Understand rule: Understand the negative exponent rule.\newlineThe negative exponent rule states that a−n=1ana^{-n} = \frac{1}{a^n}. We will apply this rule to the expression (3x)−3(3x)^{-3}.
  2. Apply rule: Apply the negative exponent rule to the expression.\newlineUsing the rule from Step 11, we can rewrite (3x)−3(3x)^{-3} as 1(3x)3\frac{1}{(3x)^3}.
  3. Expand denominator: Expand the expression in the denominator.\newlineNow we need to expand (3x)3(3x)^3. This means we will multiply 3x3x by itself three times: (3x)×(3x)×(3x)(3x) \times (3x) \times (3x).
  4. Calculate expression: Calculate the expanded expression.\newline(3x)×(3x)×(3x)=33×x3=27x3(3x) \times (3x) \times (3x) = 3^3 \times x^3 = 27x^3.
  5. Rewrite with expanded denominator: Rewrite the original expression with the expanded denominator.\newlineNow we can rewrite the expression from Step 22 with the result from Step 44: 1/((3x)3)1/((3x)^3) becomes 1/(27x3)1/(27x^3).

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