Let `x = 597 xx 10^(22) + 73.5 xx 10^(21)`, when x is expressed in standard form as `6.0435 xx 10^(m)`, then the value of m is

Options

A. 22
B. 23
C. 24
D. 21

Answer

To solve the problem, we need to calculate the value of \( x \) given by the expression:

\[ x = 597 \times 10^{22} + 73.5 \times 10^{21} \]

### Step 1: Rewrite the terms to have the same power of 10

To add these two terms, we need to express them with the same exponent. We can rewrite \( 597 \times 10^{22} \) as:

\[ 597 \times 10^{22} = 5970 \times 10^{21} \]

Now, we can rewrite the expression for \( x \):

\[ x = 5970 \times 10^{21} + 73.5 \times 10^{21} \]

### Step 2: Combine the terms

Now that both terms have the same power of 10, we can combine them:

\[ x = (5970 + 73.5) \times 10^{21} \]

Calculating the sum:

\[ 5970 + 73.5 = 6043.5 \]

So we have:

\[ x = 6043.5 \times 10^{21} \]

### Step 3: Convert to standard form

Next, we need to express \( x \) in standard form, which is typically written as \( a \times 10^m \) where \( 1 \leq a < 10 \). To convert \( 6043.5 \) into standard form, we need to shift the decimal point to the left:

\[ 6043.5 = 6.0435 \times 10^3 \]

Thus, we can write:

\[ x = 6.0435 \times 10^3 \times 10^{21} \]

### Step 4: Combine the powers of 10

Now, we combine the powers of 10:

\[ x = 6.0435 \times 10^{21 + 3} = 6.0435 \times 10^{24} \]

### Step 5: Identify the value of \( m \)

From the expression \( 6.0435 \times 10^{24} \), we can see that \( m = 24 \).

### Final Answer

The value of \( m \) is:

\[ \boxed{24} \]