Exponents and Powers – Key Vocabulary

Vocabulary flashcards reviewing fundamental terms and rules related to exponents, negative exponents, and scientific notation introduced in the lecture.

Exponent

A number that tells how many times the base is multiplied by itself, e.g., in 10^3, the exponent is 3.

Power

The entire expression that represents repeated multiplication of a base, such as 2^5 or 10^−2.

Base (of a power)

The number that is repeatedly multiplied; in 3^4, the base is 3.

Positive Exponent

An exponent greater than zero indicating repeated multiplication of the base, e.g., 2^4 = 2×2×2×2.

Negative Exponent

An exponent less than zero that indicates the reciprocal of the positive power: a^−m = 1 / a^m for non-zero a.

Zero Exponent Rule

For any non-zero number a, a^0 = 1.

Multiplicative Inverse

Two numbers whose product is 1; a^−m is the multiplicative inverse of a^m.

Product of Powers Rule

When multiplying like bases, add the exponents: a^m × a^n = a^(m+n).

Quotient of Powers Rule

When dividing like bases, subtract the exponents: a^m ÷ a^n = a^(m−n).

Power of a Power Rule

Raising a power to another power multiplies the exponents: (a^m)^n = a^(m·n).

Product to a Power Rule

A product raised to a power distributes the exponent: (ab)^m = a^m b^m.

Expanded Form (with exponents)

Writing a number as a sum of products of digits and powers of 10, e.g., 1425 = 1×10^3 + 4×10^2 + 2×10^1 + 5×10^0.

Scientific (Standard) Form

Expressing a number as k × 10^n where 1 ≤ k < 10 and n is an integer, e.g., 150 000 000 000 = 1.5 × 10^11.

Very Large Number

A number whose absolute value is much greater than 1, often written with a large positive power of 10 in standard form.

Very Small Number

A number between 0 and 1 that is expressed using a negative power of 10 in standard form, e.g., 0.000007 = 7 × 10^−6.

Reciprocal of a Power

The reciprocal of a^m is a^−m, because a^m × a^−m = 1.

Simplifying Exponents

The process of applying exponent laws to rewrite expressions in a reduced or single-power form.

Converting Large Numbers to Standard Form

Move the decimal left until one non-zero digit remains before it, counting moves as positive exponent of 10.

Converting Small Numbers to Standard Form

Move the decimal right until one non-zero digit remains before it, counting moves as negative exponent of 10.

Power of Ten

A number of the form 10^n where n is an integer; each increment of n shifts the decimal point one place.

Reciprocal of 10^n

Equal to 10^−n; for example, 1/1000 = 10^−3.

Unit Conversion with Exponents

Using powers of ten to compare or add measurements (e.g., distances Earth-Sun and Earth-Moon) by matching exponents.