If `800xx(x^3)^(2)=8xx10^8`, then x=

Options

A. `6`
B. `4`
C. `3`
D. `10`

Answer

To solve the equation \( 800 \cdot x^{(3^2)} = 8 \cdot 10^8 \), we will follow these steps:

### Step 1: Simplify the left side
We know that \( 3^2 = 9 \), so we can rewrite the equation as:
\[ 800 \cdot x^9 = 8 \cdot 10^8 \]

### Step 2: Divide both sides by 800
To isolate \( x^9 \), we divide both sides by 800:
\[ x^9 = \frac{8 \cdot 10^8}{800} \]

### Step 3: Simplify the right side
Now, we can simplify \( \frac{8}{800} \):
\[ \frac{8}{800} = \frac{1}{100} = 10^{-2} \]
Thus, we have:
\[ x^9 = 10^{-2} \cdot 10^8 \]

### Step 4: Combine the powers of 10
Using the property of exponents \( a^m \cdot a^n = a^{m+n} \):
\[ x^9 = 10^{-2 + 8} = 10^6 \]

### Step 5: Take the ninth root of both sides
To solve for \( x \), we take the ninth root of both sides:
\[ x = (10^6)^{\frac{1}{9}} = 10^{\frac{6}{9}} = 10^{\frac{2}{3}} \]

### Step 6: Convert to decimal form (if necessary)
The value \( 10^{\frac{2}{3}} \) can be approximated or left in exponent form. If we need a decimal approximation, we can calculate:
\[ 10^{\frac{2}{3}} \approx 4.64 \]

Thus, the final answer is:
\[ x = 10^{\frac{2}{3}} \text{ or approximately } 4.64 \]