Question

Simplify this expression. Show all work/steps
3√64/27^1/3

Answer 1

3√64/27-1/3

Answer 2

To simplify the expression \( \frac{3\sqrt{64}}{27^{1/3}} \), we can follow these steps:

### Step 1: Simplify the numerator
First, we simplify \( 3\sqrt{64} \).

Since \( 64 = 8^2 \), we can write:
\[
\sqrt{64} = 8
\]
So,
\[
3\sqrt{64} = 3 \times 8 = 24
\]

### Step 2: Simplify the denominator
Next, we simplify \( 27^{1/3} \).

We know that \( 27 = 3^3 \), so:
\[
27^{1/3} = (3^3)^{1/3} = 3^{3 \cdot \frac{1}{3}} = 3^1 = 3
\]

### Step 3: Combine the simplified numerator and denominator
Now we substitute back into the original expression:
\[
\frac{3\sqrt{64}}{27^{1/3}} = \frac{24}{3}
\]

### Step 4: Perform the division
Now we divide:
\[
\frac{24}{3} = 8
\]

### Final Result
The simplified expression is:
\[
\boxed{8}
\]

Answer 3

To simplify the expression \( 3\sqrt{64}/27 - \frac{1}{3} \), we can follow these steps:

### Step 1: Simplify the square root in the numerator
First, we simplify \( \sqrt{64} \):
\[
\sqrt{64} = 8
\]

So, the expression \( 3\sqrt{64} \) becomes:
\[
3 \cdot 8 = 24
\]

### Step 2: Substitute back into the expression
Now we can rewrite the expression as:
\[
\frac{24}{27} - \frac{1}{3}
\]

### Step 3: Simplify the fraction \(\frac{24}{27}\)
The fraction \( \frac{24}{27} \) can be simplified. Both the numerator and denominator can be divided by 3:
\[
\frac{24 \div 3}{27 \div 3} = \frac{8}{9}
\]

So now our expression is:
\[
\frac{8}{9} - \frac{1}{3}
\]

### Step 4: Find a common denominator
To subtract these fractions, we need a common denominator. The least common multiple of 9 and 3 is 9. We can rewrite \( \frac{1}{3} \) with a denominator of 9:
\[
\frac{1}{3} = \frac{1 \cdot 3}{3 \cdot 3} = \frac{3}{9}
\]

### Step 5: Perform the subtraction
Now we substitute back into the expression:
\[
\frac{8}{9} - \frac{3}{9} = \frac{8 - 3}{9} = \frac{5}{9}
\]

### Final Result
The simplified expression is:
\[
\boxed{\frac{5}{9}}
\]