Use exponents to condense the expression below.

Question

x, dot, x, dot, x, dot, x, dot, x, dot, y, dot, y, dot, y, dot, y, dot, z, dot, z, dot, z
x⋅x⋅x⋅x⋅x⋅y⋅y⋅y⋅y⋅z⋅z⋅z

Answer 1

To condense the expression \( x \cdot x \cdot x \cdot x \cdot x \cdot y \cdot y \cdot y \cdot y \cdot z \cdot z \cdot z \) using exponents, we count the number of times each variable appears:

• The variable \( x \) appears 5 times, which can be written as \( x^5 \).
• The variable \( y \) appears 4 times, which can be written as \( y^4 \).
• The variable \( z \) appears 3 times, which can be written as \( z^3 \).

Putting this all together, the condensed expression is:

\[ x^5 \cdot y^4 \cdot z^3 \]

If desired, this can also be written as:

\[ x^5 y^4 z^3 \]

This represents the same quantity without the dots.