Justine tried to evaluate an expression. Here is her work:

Question

10–4+2(4)2
=
Step 110–4+82
=
Step 210–4+64
=
Step 36+64
=
Step 470
Is Justine's work correct
Justine tried to evaluate an expression. Here is her work:
10–4+2(4)2
=
Step 110–4+82
=
Step 210–4+64
=
Step 36+64
=
Step 470
Is Justine's work correct?

Answer 1

Let's evaluate the expression step by step to check Justine's work:

The expression is $10-4+2(4{)}^2$.

1. First, calculate $(4{)}^2$: $$(4{)}^2=16$$ So now our expression is: $$10-4+2\cdot 16$$

2. Next, calculate $2\cdot 16$: $$2\cdot 16=32$$ Now the expression is: $$10-4+32$$

3. Now we perform the calculations from left to right:

   • First, calculate $10-4$: $$10-4=6$$
   • Now replace it in the expression: $$6+32$$
   • Finally, calculate $6+32$: $$6+32=38$$

Thus, the correct value of the expression $10-4+2(4{)}^2$ is $38$.

Now let's analyze Justine's steps:

1. She began with $10-4+2(4{)}^2$, which is correct.
2. She mistakenly moved to $10-4+8^2$ instead of $10-4+32$ after calculating $2(4{)}^2$.
3. She continued on with incorrect calculations leading to a final incorrect answer of $70$.

So, Justine's work is incorrect, and the correct answer should be $38$.