Exponents and Radicals

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 x 2 x 2 = 8).

Front

What does it mean to square a number?

Back

To square a number means to raise it to the power of 2. For example, squaring 4 (4^2) means 4 x 4 = 16.

Front

What is a radical?

Back

A radical is a symbol that represents the root of a number. The most common radical is the square root, denoted by √. For example, √16 = 4.

Front

What is the square root of 25?

Back

The square root of 25 is 5, because 5 x 5 = 25.

Front

How do you simplify the expression 2^4 x 2^3?

Back

To simplify, add the exponents: 2^(4+3) = 2^7 = 128.

Front

What is the value of 3^0?

Back

Any non-zero number raised to the power of 0 is 1. Therefore, 3^0 = 1.

Front

What is the product of powers property?

Back

The product of powers property states that when multiplying two powers with the same base, you add the exponents. For example, a^m x a^n = a^(m+n).

Front

What is the quotient of powers property?

Back

The quotient of powers property states that when dividing two powers with the same base, you subtract the exponents. For example, a^m / a^n = a^(m-n).

Front

What is the power of a power property?

Back

The power of a power property states that when raising a power to another power, you multiply the exponents. For example, (a^m)^n = a^(m*n).

Front

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

Back

Using the power of a power property, (2^3)^2 = 2^(3*2) = 2^6 = 64.