Question

Tasha used the pattern in the table to find the value of 4 Superscript negative 4. Powers of 4 Value 4 squared 16 4 Superscript 1 4 4 Superscript 0 1 4 Superscript negative 1 One-fourth 4 Superscript negative 2 StartFraction 1 Over 16 EndFraction She used these steps. Step 1 Find a pattern in the table. The pattern is to divide the previous value by 4 when the exponent decreases by 1. Step 2 Find the value of 4 Superscript negative 3. 4 Superscript negative 3 = StartFraction 1 Over 16 EndFraction divided by 4 = StartFraction 1 Over 16 EndFraction times one-fourth = StartFraction 1 Over 64 EndFraction Step 3 Find the value of 4 Superscript negative 4. 4 Superscript negative 4 = StartFraction 1 Over 64 EndFraction divided by 4 = StartFraction 1 Over 64 EndFraction times one-fourth = StartFraction 1 Over 256 EndFraction Step 4 Rewrite the value for 4 Superscript negative 4. StartFraction 1 Over 256 EndFraction = negative StartFraction 1 Over 4 Superscript negative 4 EndFraction In which step did Tasha make the first error? Step 1 Step 2 Step 3 Step 4

Answer 1

Explanation:

First error step 4

Answer 2

Step 4

Explanation:

The table is given below

`\left|\begin{array}c$Powers of 4 &$Value\\---&---\\4^2&16\\4^1&4\\4^0&1\\4^(-1)&\frac14\\4^(-2)&(1)/(16)\end{array}\right|`

Tasha wants to find the value of
`4^(-4)`.

Her steps are:

Step 1: Find a pattern in the table.

The pattern is to divide the previous value by 4 when the exponent decreases by 1.

Step 2: Find the value of
`4^(-3)`.

`4^(-3)=(1)/(16) / 4= (1)/(16) * (1)/(4)= (1)/(64)`

Step 3: Find the value of
`4^(-4)`.

`4^(-4)= (1)/(64) / 4 = (1)/(64) * (1)/(4)= (1)/(256)`

Step 4: Rewrite the value for
`4^(-4)`.

`(1)/(256) = -(1)/(4^(-4))`

Tasha made her first error in Step 4. The correct step is:

`(1)/(256) = (1)/(4^(4))`