Answer:
Step 4
Step-by-step explanation:
The table is given below
[tex]\left|\begin{array}{c|c}$Powers of 4 &$Value\\---&---\\4^2&16\\4^1&4\\4^0&1\\4^{-1}&\dfrac14\\4^{-2}&\dfrac{1}{16}\end{array}\right|[/tex]
Tasha wants to find the value of [tex]4^{-4}[/tex].
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 [tex]4^{-3}[/tex].
[tex]4^{-3}=\dfrac{1}{16} \div 4= \dfrac{1}{16} \times \dfrac{1}{4}= \dfrac{1}{64}[/tex]
Step 3: Find the value of [tex]4^{-4}[/tex].
[tex]4^{-4}= \dfrac{1}{64} \div 4 = \dfrac{1}{64} \times \dfrac{1}{4}= \dfrac{1}{256}[/tex]
Step 4: Rewrite the value for [tex]4^{-4}[/tex].
[tex]\dfrac{1}{256} = -\dfrac{1}{4^{-4}}[/tex]
Tasha made her first error in Step 4. The correct step is:
[tex]\dfrac{1}{256} = \dfrac{1}{4^{4}}[/tex]
