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Write the following expression without negative exponents and without parentheses. (-4x)^(-3) Answer:

Write the following expression without negative exponents and without parentheses.\newline(−4x)−3 (-4 x)^{-3} \newlineAnswer:

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Full solution

Q. Write the following expression without negative exponents and without parentheses.\newline(−4x)−3 (-4 x)^{-3} \newlineAnswer:
  1. Understand Negative Exponents: Understand the properties of negative exponents. The negative exponent rule states that a−n=1ana^{-n} = \frac{1}{a^n} for any non-zero aa and positive integer nn. We will apply this rule to the expression (−4x)−3(-4x)^{-3}.
  2. Apply Negative Exponent Rule: Apply the negative exponent rule to the expression.\newlineUsing the rule from Step 11, we can rewrite (−4x)−3(-4x)^{-3} as 1((−4x)3)\frac{1}{((-4x)^3)}.
  3. Expand Denominator Expression: Expand the expression in the denominator.\newlineNow we need to raise (−4x)(-4x) to the power of 33. This means we will multiply −4x-4x by itself three times: (−4x)×(−4x)×(−4x)(-4x) \times (-4x) \times (-4x).
  4. Calculate Denominator Expression: Calculate the expression in the denominator.\newlineWhen we multiply −4x-4x by itself three times, we get −4x×−4x×−4x=−64x3-4x \times -4x \times -4x = -64x^3 because (−4)3=−64(-4)^3 = -64 and (x)3=x3(x)^3 = x^3.
  5. Write Final Expression: Write the final expression without negative exponents.\newlineThe final expression without negative exponents is 1(−64x3)\frac{1}{(-64x^3)}.

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