Powers and Exponents (Part 2)

This page delves into the properties of powers and introduces scientific notation. It covers the rules for working with negative numbers raised to powers and essential properties for manipulating expressions with exponents.

Definition: Scientific notation expresses numbers in the form a × 10^n, where 1 ≤ a < 10 and n is an integer.

Example: -2^4 can be calculated in two ways:

1. -2 × 2 × 2 × 2 = -16
2. (-2) × (-2) × (-2) × (-2) = +16

Highlight: Key properties of exponents include:

• (a^n)^p = a^(n×p)
• a^n × a^p = a^(n+p)
• a^n ÷ a^p = a^(n-p)
• (a × b)^n = a^n × b^n

Example: 0.004176 can be written in scientific notation as 4.176 × 10^-3

Powers and Exponents (Part 1)

This page introduces fundamental concepts of powers and exponents in mathematics. The content explains how powers represent repeated multiplication of the same number and introduces key notations.

Definition: A power is the product of a number multiplied by itself a certain number of times, written as a^n where 'a' is the base and 'n' is the exponent.

Example: 10^6 = 1,000,000 (one million), showing how powers of 10 create large numbers efficiently.

Vocabulary: Negative exponents indicate the reciprocal of the positive exponent, meaning a^-n = 1/a^n.

Highlight: Powers of 10 are particularly important and correspond to common metric prefixes:

• Giga (10^9)
• Mega (10^6)
• Kilo (10^3)
• Milli (10^-3)
• Micro (10^-6)
• Nano (10^-9)