Question

Expression to represente a number with exponents

Answer 1

To represent a number using exponents, you can use the form:

\[
a^n
\]

where:

- \( a \) is the base (a number that is being multiplied),
- \( n \) is the exponent (the number of times the base is multiplied by itself).

For example:

- \( 2^3 \) represents \( 2 \times 2 \times 2 = 8 \).
- \( 5^2 \) represents \( 5 \times 5 = 25 \).
- \( 10^0 \) equals \( 1 \) (any non-zero number raised to the power of 0 is 1).

You can also represent larger numbers using exponentiation, such as:

- \( 1000 \) can be represented as \( 10^3 \) (since \( 10 \times 10 \times 10 = 1000 \)).

If you want to represent a number as a product of its prime factorization, you can express it in the following form:

\[
p_1^{e_1} \times p_2^{e_2} \times \ldots \times p_k^{e_k}
\]

where \( p_1, p_2, \ldots, p_k \) are the prime factors and \( e_1, e_2, \ldots, e_k \) are their respective exponents.

For instance, the number \( 60 \) can be represented as:

\[
60 = 2^2 \times 3^1 \times 5^1
\]

This means \( 60 \) is made up of \( 2 \) raised to the power of \( 2 \), \( 3 \) raised to the power of \( 1 \), and \( 5 \) raised to the power of \( 1 \).