nsider the equation 4^3⋅(64−−√3^)2=4^6

Question

. Is this equation true or false? Enter 1 for true or 2 for false.(1 point)

Answer 1

To determine if the equation \(4^3 \cdot (64^{1/3})^2 = 4^6\) is true or false, let's simplify both sides of the equation step by step.

First, simplify the left side:

1. Compute \(64^{1/3}\): \[ 64 = 4^3 \quad \text{(since \(4^3 = 64\))} \] So, \[ 64^{1/3} = (4^3)^{1/3} = 4^{3 \cdot \frac{1}{3}} = 4^1 = 4. \]

2. Now substitute \(64^{1/3}\) back into the equation: \[ 4^3 \cdot (64^{1/3})^2 = 4^3 \cdot 4^2. \]

3. Combine the exponents: \[ 4^3 \cdot 4^2 = 4^{3+2} = 4^5. \]

Now we have simplified the left side to \(4^5\).

Next, simplify the right side: \[ 4^6 \text{ is already in simplified form.} \]

Now we compare both sides: \[ 4^5 \neq 4^6. \]

Since \(4^5\) is not equal to \(4^6\), the original equation is false.

Thus, the answer is: \[ \boxed{2} \]