Simplify this expression. Show all work/steps

Question

3√64/27^1/3

Answer 1

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 2

3√64/27-1/3

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: \[ \boxed{\frac{5}{9}} \]