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.