Simplify : `((6.25)^((1)/(2))xx(0.0144)^((1)/(2))+1)/((0.027)^((1)/(3))xx(81)^((1)/(4)))`

Options

A. `0.14`
B. `1.4`
C. `1`
D. `1.bar(4)`

Answer

To simplify the expression \(\frac{(6.25)^{\frac{1}{2}} \times (0.0144)^{\frac{1}{2}} + 1}{(0.027)^{\frac{1}{3}} \times (81)^{\frac{1}{4}}}\), we will follow these steps:

### Step 1: Simplify the numerator
First, we simplify the terms in the numerator:

1. Calculate \((6.25)^{\frac{1}{2}}\):
\[ (6.25)^{\frac{1}{2}} = \sqrt{6.25} = 2.5 \]

2. Calculate \((0.0144)^{\frac{1}{2}}\):
\[ (0.0144)^{\frac{1}{2}} = \sqrt{0.0144} = 0.12 \]

3. Multiply these results:
\[ 2.5 \times 0.12 = 0.3 \]

4. Add 1 to this result:
\[ 0.3 + 1 = 1.3 \]

### Step 2: Simplify the denominator
Now, we simplify the terms in the denominator:

1. Calculate \((0.027)^{\frac{1}{3}}\):
\[ (0.027)^{\frac{1}{3}} = \sqrt[3]{0.027} = 0.3 \]

2. Calculate \((81)^{\frac{1}{4}}\):
\[ (81)^{\frac{1}{4}} = \sqrt[4]{81} = 3 \]

3. Multiply these results:
\[ 0.3 \times 3 = 0.9 \]

### Step 3: Combine the results
Now we can combine the results from the numerator and the denominator:

\[ \frac{1.3}{0.9} \]

### Step 4: Simplify the fraction
To simplify \(\frac{1.3}{0.9}\):

1. Multiply both the numerator and the denominator by 10 to eliminate the decimal:
\[ \frac{1.3 \times 10}{0.9 \times 10} = \frac{13}{9} \]

### Final Result
Thus, the simplified expression is:
\[ \frac{13}{9} \]

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