Powers and Exponents

Senin, 12 Juni 2023

Perfect squares like 1, 4, 9, and 16 can be represented by a square array of dots.

A perfect square is the product of a number and itself. For example, 16 is a perfect square because 16 = 4 × 4. The expression 4 × 4 can be written using exponents. An exponent tells how many times a number, called the base, is used as a factor. Numbers that are expressed using exponents are called powers. The expression 4 × 4 can be written as 4².

Example

Write each expression using exponents.

 

1.     2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2

 

Alternative Solutions:

 

The base is 2. It is a factor 5 times

2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 2⁵

 

 

2.     m ⋅ m ⋅ m ⋅ m

 

Alternative Solutions:

 

The base is m. It is a factor 4 times

m ⋅ m ⋅ m ⋅ m = m⁴

 

 

3.     7

 

Alternative Solutions:

 

The base is 7. It is a factor 1 times

7 = 7¹

 

Example

 

4.     Write (2)(2)(2)(–5)(–5) using exponents.

 

Alternative Solutions:

 

Use the Associative Property to group the factors with like bases.

(2)(2)(2)(–5)(–5) = [(2)(2)(2)][(–5)(–5)]

                          = (2)³(–5)²

 

You can use the definition of exponent to write a power as a multiplication expression.

 

Example

Write each power as a multiplication expression.

 

5.     10²

 

Alternative Solutions:

 

The base is 10. The exponent 2 means that 10 is a factor 2 times.

10² = 10 ⋅ 10

 

6.     b³

 

Alternative Solutions:

 

The base is b. The exponent 3 means that b is a factor 3 times.

b³ = b ⋅ b ⋅ b

 

7.     10x²y⁴

 

Alternative Solutions:

 

10 is used as a factor once, x is used twice, and y is used 4 times.

10x²y⁴ = 10 ⋅ x ⋅ x ⋅ y ⋅ y ⋅ y ⋅ y

 

 

You can also use the definition of exponent to evaluate expressions.

 

Example

Science Link

 

8.     The distance between the Earth and the Sun is about 10⁸ kilometers. Write this number as a multiplication expression and then evaluate the expression.

 

Alternative Solutions:

 

108 = 10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10

  = 100,000,000

 

The distance between Earth and the sun is about 100 million kilometers.

 

When an expression contains an exponent, simplify the expression using the rules for order of operations.

In any expression, an exponent goes with the number or the quantity in parentheses that immediately precedes it.

Example

Evaluate each expression.

 

9.     4m³ if m = 2

 

Alternative Solutions:

 

10.   3x + y² if x = –2 and y = –3

 

Alternative Solutions:

 

 

 

Sumber

Labels: Mathematician

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