Questions: Simplify. Assume z ≠ 0. (z^(-6))^7

Simplify. Assume z ≠ 0. (z^(-6))^7
Transcript text: Simplify. Assume z $\neq 0$. \[ \left(z^{-6}\right)^{7} \]
failed

Solution

failed
failed

Solution Steps

To simplify the expression \((z^{-6})^{7}\), we can use the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\). Applying this property, we multiply the exponents \(-6\) and \(7\).

Step 1: Apply the Power of a Power Property

To simplify the expression \((z^{-6})^{7}\), we use the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\). Here, \(a = z\), \(m = -6\), and \(n = 7\).

Step 2: Multiply the Exponents

Multiply the exponents \(-6\) and \(7\) to find the new exponent for \(z\): \[ -6 \times 7 = -42 \]

Final Answer

\(\boxed{z^{-42}}\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Which of the following statements is correct? Multiple Choice Meiosis involves two divisions and produces four nonidentical gametes. Meiosis involves one division and produces two nonidentical gametes. Mitosis involves one division and produces two nonidentical gametes. Mitosis involves two divisions and produces four identical gametes.
failedAnswered
What condition causes aluminum branch circuit wiring to be unsafe? overheating at poor connections the absence of ground wires the use of COPALUM crimp connectors wire gauges too small for amperage
failedAnswered
Patient teaching included the need to increase protein and calories. A woman is questioning how to increase the protein and calories of her husband's diet. Which of the following strategies might the nurse suggest? Top baked potatoes with low-fat sour cream Add whipped cream to coffee Increase fruits topped with sugar or honey Substitute whole milk for water in recipes
failedAnswered
Maximus is playing a game. When he rolls the dice he wins if he gets an even number and loses if he gets an odd number. Which of the following statements is FALSE? The count of rolling an even number can be approximated with a normal distribution The count of rolling an odd number can be approximated with a normal distribution The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution Rolling an even number is considered a success
failedAnswered
Consider the function: g(x)=x^2-7 x+13 Find and simplify g(x-11). [Hint: See § 2.1, Example 5d.]