Question

Write each expression using exponents.

$\frac{\mathbf{1}}{\mathbf{3}}\mathbf{\cdot }\frac{\mathbf{1}}{\mathbf{3}}\mathbf{\cdot }\frac{\mathbf{1}}{\mathbf{3}}\mathbf{\cdot }\frac{\mathbf{1}}{\mathbf{3}}\mathbf{\cdot }\frac{\mathbf{1}}{\mathbf{3}}\mathbf{\cdot }\frac{\mathbf{1}}{\mathbf{3}}\mathbf{\cdot }\frac{\mathbf{1}}{\mathbf{3}}\mathbf{\cdot }\frac{\mathbf{1}}{\mathbf{3}}$

Short answer

The required expression is represented by ${\left(\frac{1}{3}\right)}^{\mathbf{8}}$.

Step-by-step solution

Step 1. Count the factors of the provided fraction.

The provided fraction is$\frac{1}{3}$ and the count associated with its factors is represented by 8.

Step 2. Take the help of obtained count and form the required exponential form.

Write the exponential form by taking the provided fraction as base and the count associated with its factors as exponent on it.

${\left(\frac{1}{3}\right)}^8$

Step 3. Write the conclusion.

The obtained expression contains contain exponent which means that ${\left(\frac{1}{3}\right)}^8$is the required expression.