Question

Simplify (−5z)^3. Write your answer using only positive exponents. Evaluate any numerical powers.

Answer 1

Simplifying (−5z)^3 involves cubing the numerical term -5, resulting in -125, and raising z to the power of 3, resulting in z^3. The simplified expression is -125z^3.

Step-by-step explanation:

To simplify (−5z)^3, we need to apply the cubing operation to both the numerical coefficient and the variable individually. When cubing a negative number, the sign will stay negative, as a negative number multiplied by itself an odd number of times remains negative. So, the cubing of the numerical coefficient -5 will give us -5×-5×-5, which equals -125. For the variable z, we use the rule that when you raise a power to a power, you multiply the exponents. In this case, z has an implied exponent of 1, so cubing of exponentials means we do 1×3, which gives us an exponent of 3 for z.

Thus, (−5z)^3 simplifies to -125z^3. This is the simplified expression with only positive exponents.

Answer 2

`-125\ z^3`

Step-by-step explanation:

To simplify:

`(-5\ z)^3`

Using Power of product rule [
`(a\ b)^x=a^xb^x` ]

⇒
`(-5)^3(z)^3`

Evaluating the numerical powers.

⇒
`(-5* -5 * -5)\ z^3`

⇒
`-125\ z^3`

The expression cannot be simplified any further, so that would be the final form.