if `10^(k-3)=m,` then `10^(k)=`

Options

A. `1,000m`
B. `m+1,000`
C. `(m)/(1,000)`
D. `m-1,000`

Answer

To solve the equation \( 10^{k-3} = m \) and find the value of \( 10^k \), we can follow these steps:

### Step 1: Rewrite the equation using properties of exponents
We know that \( 10^{k-3} \) can be expressed as:
\[ 10^{k-3} = \frac{10^k}{10^3} \]
This is based on the property of exponents that states \( a^{x-y} = \frac{a^x}{a^y} \).

### Step 2: Set the rewritten equation equal to \( m \)
From the original equation, we have:
\[ \frac{10^k}{10^3} = m \]

### Step 3: Multiply both sides by \( 10^3 \)
To isolate \( 10^k \), we multiply both sides of the equation by \( 10^3 \):
\[ 10^k = m \cdot 10^3 \]

### Step 4: Simplify the expression
Since \( 10^3 = 1000 \), we can rewrite the equation as:
\[ 10^k = 1000m \]

### Final Answer
Thus, the value of \( 10^k \) is:
\[ 10^k = 1000m \]

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