Exponents, Perfect Squares, and Powers of 10

Vocabulary flashcards covering exponents, special exponent rules, perfect squares, and powers of 10.

Base

The number that is repeatedly multiplied by itself in an exponential expression (for example, in $7^3$, $7$ is the base).

Exponent

The number that indicates how many times the base is multiplied by itself (for example, in $7^3$, $3$ is the exponent).

Base to the ZERO Power

A rule stating that any base to the zero power is always equal to $1$ (for example, $9^0 = 1$), except $0^0$ which is undefined.

Base to the FIRST Power

A rule stating that any base to the first power is always equal to the base itself (for example, $8^1 = 8$).

Squared

A term used to describe raising a base to the second power.

Cubed

A term used to describe raising a base to the third power.

Perfect Square

The product of two equal integers, which represents the amount of boxes or area inside a square having equal width and length.

Zero as a Perfect Square

Zero is considered a perfect square because $0$ times itself is $0$, even though it does not form a physical square.

Powers of 10

Expressions with a base of $10$ where the exponent directly matches the number of zeros in standard form (for example, $10^6 = 1,000,000$).

Seven Squared

An expression evaluated as $7 \times 7$, which equals $49$ (written as $7^2 = 49$).

Twelve Cubed

An expression evaluated as $12 \times 12 \times 12$, which equals $1,728$ (written as $12^3 = 1,728$).

Equivalent Value of $6^4$

An expression representing $6 \times 6 \times 6 \times 6$, which can also be expressed as $36 \times 36$, $216 \times 6$, or $1,296$.

Place Value Chart Representation of $10^5$

The number $100,000$, represented in a place value chart with a $1$ in the Hundred-thousands column followed by zeros in Ten-thousands, Thousands, Hundreds, Tens, and Ones.