Write expressions for repeated operations

A repeated operation is represented compactly by recognizing its structure: equal additions can be written as multiplication with a whole-number coefficient, and repeated multiplication of the same factor can be written with a whole-number exponent where appropriate. The expression must preserve the intended quantity and operation order, distinguishing forms such as $3x$ , $x+3$ , and $3(x+2)$ ; advanced exponent laws and generalized symbolic cases are not included.

Detailed Explanation: Write expressions for repeated operations

A repeated operation can often be written more briefly.

Repeated addition of the same amount becomes multiplication.
Repeated multiplication of the same factor becomes an exponent.

Worked example

A box contains $(x+2)$ pencils. There are $3$ identical boxes. Write an expression for the total number of pencils.

Step 1: Write the repeated addition.

Each box has $(x+2)$ pencils, so add that amount $3$ times:

(x+2)+(x+2)+(x+2)

Step 2: Replace the repeated addition with multiplication.

There are $3$ groups of $(x+2)$ , so write:

\boxed{3(x+2)}

The parentheses are important because the whole quantity $(x+2)$ is repeated.

$(3(x+2))$ means $3$ groups of $(x+2)$ .
$(3x)$ means $3$ groups of only $x$ .
$(x+3)$ means $3$ is added to $x$ .

For repeated multiplication, use an exponent. For example,

2\cdot2\cdot2\cdot2=2^4

The exponent $4$ tells how many times the factor $2$ is used.

Learn by doing: Write expressions for repeated operations

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Exponents - Expanded Form

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