Q. Write the following expression without negative exponents and without parentheses.(−4x)−3Answer:
Understand Negative Exponents: Understand the properties of negative exponents. The negative exponent rule states that a−n=an1 for any non-zero a and positive integer n. We will apply this rule to the expression (−4x)−3.
Apply Negative Exponent Rule: Apply the negative exponent rule to the expression.Using the rule from Step 1, we can rewrite (−4x)−3 as ((−4x)3)1.
Expand Denominator Expression: Expand the expression in the denominator.Now we need to raise (−4x) to the power of 3. This means we will multiply −4x by itself three times: (−4x)×(−4x)×(−4x).
Calculate Denominator Expression: Calculate the expression in the denominator.When we multiply −4x by itself three times, we get −4x×−4x×−4x=−64x3 because (−4)3=−64 and (x)3=x3.
Write Final Expression: Write the final expression without negative exponents.The final expression without negative exponents is (−64x3)1.