Q8. - Algebra 1

Question

Write each expression using exponents.

$\frac{\mathbf{x}}{\mathbf{y}}\mathbf{\cdot }\frac{\mathbf{x}}{\mathbf{y}}\mathbf{\cdot }\frac{\mathbf{x}}{\mathbf{y}}\mathbf{\cdot }\frac{\mathbf{x}}{\mathbf{y}}\mathbf{\cdot }\frac{\mathbf{w}}{\mathbf{z}}\mathbf{\cdot }\frac{\mathbf{w}}{\mathbf{z}}$

Step-by-Step Solution

Answer

The required expression is represented by ${\left(\frac{x}{y}\right)}^{\mathbf{4}}{\left(\frac{w}{z}\right)}^{\mathbf{2}}$. 

Step 1. Count the factors of the provided fractions.

The provided fractions are $\frac{x}{y}$ and $\frac{w}{z}$. The count associated with the factors of $\frac{x}{y}$ and $\frac{w}{z}$ is represented by 4 and 2 respectively.

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

Write the exponential form by taking the provided fractions as base and the count associated with their respective factors as exponent on them.

${\left(\frac{x}{y}\right)}^4{\left(\frac{w}{z}\right)}^2$

Step 3. Write the conclusion.

The obtained expression contains contain exponents which means that ${\left(\frac{x}{y}\right)}^4{\left(\frac{w}{z}\right)}^2$ is the required expression.