Write and expression using an exponent equivalent to 5x5x5x5
The Correct Answer and Explanation is:
Expression Using an Exponent:
The expression equivalent to ( 5 \times 5 \times 5 \times 5 ) is written as ( 5^4 ). This is because the base, ( 5 ), is multiplied by itself ( 4 ) times.
Correct Answer:
The value of ( 5^4 ) is:
[
5^4 = 5 \times 5 \times 5 \times 5 = 25 \times 5 = 125 \times 5 = 625
]
Thus, ( 5^4 = 625 ).
Explanation:
Exponents, also called powers, are a shorthand way to express repeated multiplication of a number by itself. In the expression ( 5^4 ):
- Base (( 5 )): The number being multiplied repeatedly.
- Exponent (( 4 )): The number of times the base is multiplied by itself.
The exponent tells us to use the base as a factor ( 4 ) times. This simplifies long multiplication, making it easier to write and calculate. Instead of ( 5 \times 5 \times 5 \times 5 ), we use ( 5^4 ), which is more compact.
Calculation Step-by-Step:
- Start with ( 5 \times 5 = 25 ).
- Multiply ( 25 ) by ( 5 ), resulting in ( 125 ).
- Multiply ( 125 ) by ( 5 ), resulting in ( 625 ).
So, ( 5^4 = 625 ).
Importance of Exponents:
Exponents are widely used in mathematics and science to simplify calculations involving large numbers, such as in areas like physics, engineering, and computer science. For example:
- In geometry, exponents are used to calculate areas and volumes, such as ( r^2 ) for the area of a circle.
- In finance, they represent compound interest over time, such as ( (1 + r)^n ).
Understanding exponents is essential for advancing in algebra and other higher-level math topics, as they form the foundation for working with polynomials, logarithms, and exponential functions.