Negative and Zero Exponents
This Grade 6 algebra skill from Yoshiwara Elementary Algebra introduces negative and zero exponents and their definitions. Students learn that any non-zero number raised to the power of zero equals 1, and that a negative exponent indicates the reciprocal of the base raised to the positive exponent (a^-n = 1/a^n).
Key Concepts
Property Zero as an Exponent $$a^0 = 1, \quad \text{if } a \neq 0$$.
Negative Exponents $$a^{ n} = \frac{1}{a^n} \quad \text{if } a \neq 0$$.
A negative power is the reciprocal of the corresponding positive power. A negative exponent does not mean that the power is negative. The laws of exponents apply to negative exponents.
Common Questions
What is a zero exponent?
Any non-zero number raised to the power of zero equals 1. For example, 5^0 = 1 and x^0 = 1 for any x not equal to zero.
What is a negative exponent?
A negative exponent means take the reciprocal and use a positive exponent. For example, 2^-3 = 1/2^3 = 1/8.
How do you simplify an expression with a negative exponent?
Move the factor with the negative exponent to the other side of a fraction and make the exponent positive. For example, x^-2 = 1/x^2.
Why is any number to the zero power equal to 1?
Using the quotient rule, a^n / a^n = a^(n-n) = a^0 = 1 (since any number divided by itself is 1).
Where are negative and zero exponents taught?
Negative and zero exponents are introduced in the Yoshiwara Elementary Algebra textbook for Grade 6 students.