For all nonzero y and z , `((yxx10^5)(zxx0.0001))/((yxx100,000)(zxx10^(-4)))=?`

Options

A. `10^9`
B. 10
C. 1
D. `y/z`

Answer

To solve the expression \(\frac{(y \times 10^5)(z \times 0.0001)}{(y \times 100,000)(z \times 10^{-4})}\), we will simplify it step by step.

### Step 1: Rewrite the constants in terms of powers of 10
We know that:
- \(100,000 = 10^5\)
- \(0.0001 = 10^{-4}\)

Using these conversions, we can rewrite the expression:

\[ \frac{(y \times 10^5)(z \times 10^{-4})}{(y \times 10^5)(z \times 10^{-4})} \]

### Step 2: Substitute the rewritten constants into the expression
Now, substituting the rewritten constants into the expression gives us:

\[ \frac{(y \times 10^5)(z \times 10^{-4})}{(y \times 10^5)(z \times 10^{-4})} \]

### Step 3: Cancel out the common terms
Since the numerator and denominator are identical, we can cancel them out:

\[ = 1 \]

### Final Answer
Thus, the value of the expression is \(1\).

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