Question 1

What happens when you raise a number to a negative exponent?

Accepted Answer

A negative exponent represents the multiplicative inverse (reciprocal) of the base: b^(-n) = 1 / (b^n). For example, 2^(-3) = 1 / 8 = 0.125.

Question 2

Why is any non-zero number to the power of 0 equal to 1?

Accepted Answer

From the quotient rule of exponents, b^n / b^n = b^(n - n) = b^0. Since any non-zero value divided by itself equals 1, b^0 must equal 1.

Question 3

How are fractional exponents evaluated?

Accepted Answer

A fractional exponent represents an nth root: b^(m/n) = n-th root of (b^m). For example, 16^(0.75) = 16^(3/4) = (4th root of 16)^3 = 2^3 = 8.

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