Is the equation 3−5⋅(81√4)33−4=3−6

Question

3
−
5
⋅
(
81
4
)
3
3
−
4
=
3
−
6
true or false? Select the response that correctly answers the question and provides the appropriate justification.(1 point)
Responses

False. (81−−√4)3
(
81
4
)
3
cannot be determined.
False. open paren 4

Answer 1

To determine whether the equation \( 3 - 5 \cdot \left( 81 \sqrt{4} \right)^3 - 4 = 3 - 6 \) is true or false, we will simplify both sides of the equation step by step.

Left Side:

Let's evaluate \( 81 \sqrt{4} \):

• \( \sqrt{4} = 2 \)
• So, \( 81 \sqrt{4} = 81 \cdot 2 = 162 \)

Now, we need to compute \( (162)^3 \):

• \( 162^3 = 162 \cdot 162 \cdot 162 \)

Calculating \( 162^3 \):

• \( 162^2 = 26244 \)
• Then, \( 162^3 = 162 \cdot 26244 = 4251528 \)

Now we can evaluate the left side of the equation: \[ 3 - 5 \cdot (162)^3 - 4 = 3 - 5 \cdot 4251528 - 4 \] Now calculate \( 5 \cdot 4251528 = 21257640 \): \[ 3 - 21257640 - 4 = 3 - 21257644 = -21257641 \]

Right Side:

Now for the right side: \[ 3 - 6 = -3 \]

Comparison:

Now, we compare the left side and right side:

• Left Side: \( -21257641 \)
• Right Side: \( -3 \)

Since \( -21257641 \neq -3 \), the equation is false.

Final Answer:

False.