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Write the following expression without negative exponents and without parentheses.

(-5x)^(-3)
Answer:

Write the following expression without negative exponents and without parentheses.\newline(5x)3 (-5 x)^{-3} \newlineAnswer:

Full solution

Q. Write the following expression without negative exponents and without parentheses.\newline(5x)3 (-5 x)^{-3} \newlineAnswer:
  1. Understand Negative Exponents: Understand the properties of negative exponents. The negative exponent rule states that an=1ana^{-n} = \frac{1}{a^n} for any non-zero aa and positive integer nn. We will apply this rule to the expression (5x)3(-5x)^{-3}.
  2. Apply Negative Exponent Rule: Apply the negative exponent rule to the expression.\newlineUsing the rule from Step 11, we can rewrite (5x)3(-5x)^{-3} as 1((5x)3)\frac{1}{((-5x)^3)}.
  3. Expand Denominator: Expand the expression in the denominator.\newlineNow we need to raise (5x)(-5x) to the power of 33. This means we will multiply 5x-5x by itself three times: (5x)×(5x)×(5x)(-5x) \times (-5x) \times (-5x).
  4. Calculate Denominator: Calculate the expression in the denominator.\newline(5x)×(5x)×(5x)=5×5×5×x×x×x=125x3(-5x) \times (-5x) \times (-5x) = -5 \times -5 \times -5 \times x \times x \times x = 125x^3 because a negative number multiplied by itself an odd number of times remains negative, and xx multiplied by itself three times is x3x^3.
  5. Write Final Expression: Write the final expression without negative exponents and without parentheses.\newlineThe final expression is 1125x3\frac{1}{125x^3}.

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