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 * 2 * 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 * 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

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

Back

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

Front

What is the relationship between exponents and roots?

Back

Exponents and roots are inversely related. For example, raising a number to the power of 1/n is equivalent to taking the nth root of that number (e.g., x^(1/2) = √x).

Front

What is the value of 3^0?

Back

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

Front

How do you convert a radical expression to an exponent?

Back

To convert a radical expression to an exponent, use the formula: √x = x^(1/2) and for nth roots, use x^(1/n).

Front

What is the product of powers property?

Back

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

Front

What is the quotient of powers property?

Back

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

Front

What does it mean to rationalize the denominator?

Back

Rationalizing the denominator means to eliminate any radicals in the denominator of a fraction by multiplying the numerator and denominator by a suitable radical.