Write $5 \times 5 \times 5 \times 5$ using exponents.
A) $4^5$
B) $5^5$
C) $5^4$
D) $5^2$
Answer (2)
The expression is a repeated multiplication of 5 by itself 4 times.
Repeated multiplication can be expressed using exponents.
The base is 5 and the exponent is 4, so the expression is 5 4 .
The correct option is C) 5 4 .
Explanation
Understanding the problem We are asked to express the repeated multiplication 5 × 5 × 5 × 5 using exponents.
Identifying base and exponent In exponential notation, we have a base and an exponent. The base is the number being multiplied, and the exponent is the number of times the base is multiplied by itself. In this case, the base is 5, and it is multiplied by itself 4 times.
Writing in exponential form Therefore, 5 × 5 × 5 × 5 can be written as 5 4 .
Choosing the correct option Comparing our result with the given options, we see that option C, 5 4 , is the correct answer.
Examples
Exponents are useful in many real-life situations. For example, when calculating compound interest, the formula involves exponents. If you invest P dollars at an annual interest rate r compounded n times per year, the amount A you'll have after t years is given by A = P ( 1 + n r ) n t . Exponents also appear in scientific notation, used to express very large or very small numbers, such as the distance to stars or the size of atoms.
The expression 5 × 5 × 5 × 5 can be written using exponents as 5 4 . Therefore, the correct option is C) 5 4 . Exponents simplify repeated multiplication, where in this case, 5 is the base and 4 is the exponent.
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