Exponents & Exponent Properties

Front

What is an exponent?

Back

An exponent is a number that indicates how many times to multiply the base by itself. For example, in 2^3, 2 is the base and 3 is the exponent, meaning 2 is multiplied by itself 3 times (2 × 2 × 2 = 8).

Front

What is the product of c^4 and c^3?

Back

c^7 (When multiplying powers with the same base, add the exponents: 4 + 3 = 7).

Front

What does the term 'common ratio' refer to in a geometric sequence?

Back

The common ratio is the factor by which each term in a geometric sequence is multiplied to get the next term.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the difference between any two consecutive terms in an arithmetic sequence.

Front

How do you multiply powers with the same base?

Back

To multiply powers with the same base, add their exponents.

Front

What is the value of 2^0?

Back

2^0 = 1 (Any non-zero number raised to the power of 0 is 1).

Front

What is the value of (x^3) * (x^2)?

Back

x^5 (Add the exponents: 3 + 2 = 5).

Front

What is the value of (a^5)/(a^2)?

Back

a^3 (Subtract the exponents: 5 - 2 = 3).

Front

What does r represent in the context of sequences?

Back

r represents the common ratio in a geometric sequence.

Front

What is the formula for finding the nth term of an arithmetic sequence?

Back

nth term = first term + (n-1) * common difference.