Question

which of the following expressions is equivalent to $9 - 9 \cdot 6$? $3^2 - 3^2 \cdot 2^2$ $3^2 - 3 \cdot 2^3$ $3^2 - 3 \cdot 2$ $3^2 - 3^3 \cdot 2$ skill code: 104300

Explanation:

Step1: Calculate the original expression

First, calculate \(9 - 9\times6\). According to the order of operations (PEMDAS/BODMAS), we perform multiplication first: \(9\times6 = 54\). Then subtract: \(9 - 54=-45\).

Step2: Analyze each option

• Option 1: \(3^{2}-3^{2}\times2^{2}\)

Calculate exponents first: \(3^{2} = 9\), \(2^{2}=4\). Then multiplication: \(9\times4 = 36\). Then subtraction: \(9 - 36=-27
eq - 45\).

• Option 2: \(3^{2}-3\times2^{3}\)

Calculate exponents: \(2^{3}=8\). Then multiplication: \(3\times8 = 24\). Then subtraction: \(9 - 24=-15
eq - 45\). Wait, maybe I made a mistake. Wait, original expression: \(9-9\times6=9 - 54=-45\). Wait, let's re - check the options. Wait, maybe the first option: \(3^{2}-3^{2}\times2^{2}=9-9\times4 = 9 - 36=-27\). Second option: \(3^{2}-3\times2^{3}=9-3\times8=9 - 24=-15\). Third option: \(3^{2}-3\times2=9 - 6 = 3\). Fourth option: \(3^{2}-3^{3}\times2=9-27\times2=9 - 54=-45\). Oh! I missed the fourth option. Let's re - do:

Wait, the original problem's options: Let's list all options properly.

Option 1: \(3^{2}-3^{2}\times2^{2}\)

Option 2: \(3^{2}-3\times2^{3}\)

Option 3: \(3^{2}-3\times2\)

Option 4: \(3^{2}-3^{3}\times2\)

Now, calculate each:

Original: \(9-9\times6=9-(9\times6)=9 - 54=-45\)

Option 1: \(3^{2}-3^{2}\times2^{2}=9-(9\times4)=9 - 36=-27\)

Option 2: \(3^{2}-3\times2^{3}=9-(3\times8)=9 - 24=-15\)

Option 3: \(3^{2}-3\times2=9 - 6 = 3\)

Option 4: \(3^{2}-3^{3}\times2=9-(27\times2)=9 - 54=-45\)

So the equivalent expression is \(3^{2}-3^{3}\times2\) (the fourth option, but in the given image, the checked one is probably the fourth. Wait, the user's image shows a checked box, but let's confirm the calculation.

Wait, maybe the first option was misread. Wait, the first option: \(3^{2}-3^{2}\times2^{2}\), second: \(3^{2}-3\times2^{3}\), third: \(3^{2}-3\times2\), fourth: \(3^{2}-3^{3}\times2\).

So the correct one is \(3^{2}-3^{3}\times2\) because \(3^{2}=9\), \(3^{3}=27\), \(27\times2 = 54\), \(9-54=-45\) which matches \(9 - 9\times6=-45\).

Answer:

The expression equivalent to \(9 - 9\times6\) is \(3^{2}-3^{3}\times2\) (the fourth option in the list of options provided in the problem).