Understanding the Laws of Exponents is fundamental to simplifying complex mathematical expressions and working with large numbers in scientific notation. This guide breaks down the core Exponents Formulas with clear examples derived from the provided content.
When multiplying powers with the same base, you add the exponents.
Formula: $a^m \times a^n = a^{m+n}$
Examples:
$2^5 \times 2^{10} = 2^{5+10} = 2^{15}$
$3^2 \times 3^7 = 3^{2+7} = 3^9$
$2^5 \times 2^{10} \times 2^{12} = 2^{5+10+12} = 2^{27}$
$5^{10} \times 5^2 \times 5^3 = 5^{10+2+3} = 5^{15}$
Note on Expansion:
The expression $2^3 \times 2^5$ can be written out as:
This results in 8 factors of 2, or $2^8$, which is equal to $2^{3+5}$.