Question

I’m trying to teach this to my nephew and need help

Answer 1

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We need to develop the expression

`\mleft(-(1)/(4)\mright)^3`

Step 1

Distribute the exponent to the numerator and to the denominator:

`\mleft(-(1)/(4)\mright)^3=((-1)^(3))/(4^(3))`

Step 2

Use the property

`x^n=x\cdot x\cdot x\cdot\ldots\cdot x\text{ (n factors)}`

We obtain:

`\begin{gathered} (-1)^3=(-1)\cdot(-1)\cdot(-1) \\ \\ 4^3=4\cdot4\cdot4 \end{gathered}`

Step 3

Use the properties:

• factors with the same sign result in a positive product

`(-1)\cdot(-1)=1`

• factors with opposite signs result in a negative product

`1\cdot(-1)=-1`

Thus:

`(-1)\cdot(-1)\cdot(-1)=1\cdot(-1)=-1`

Step 4

Compute the product

`4\cdot4\cdot4=16\cdot4=64`

Answer

Use the previous results to write:

`((-1)^3)/(4^3)=-(1)/(64)`