An exponent is a shorthand notation for repeated multiplication.

Exponents exponent base An exponent is a shorthand notation for repeated multiplication. 3 • 3 • 3 • 3 • 3 3 is a factor 5 times Using an exponent, this product can be written as

Exponential Notation exponent base This is called exponential notation. The exponent, 5, indicates how many times the base, 3, is a factor. Read as “three to the fifth power” or “the fifth power of three.” 3 • 3 • 3 • 3 • 3 3 is a factor 5 times

Reading Exponential Notation 4 = 41 is read as “four to the first power.” 4  4 = 42 is read as “four to the second power” or “four squared.”

Reading Exponential Notation 4  4  4 = 43 is read as “four to the third power” or “four cubed.” 4  4  4  4 = 44 is read as “four to the fourth power.”

Helpful Hint Usually, an exponent of 1 is not written, so when no exponent appears, we assume that the exponent is 1. For example, 2 = 21 and 7 = 71.

Examples Write the following numbers as a product of primes using exponents. 7056 3240

Evaluating Exponential Expressions To evaluate an exponential expression, we write the expression as a product and then find the value of the product. 35 = 3 • 3 • 3 • 3 • 3 = 243

Helpful Hint An exponent applies only to its base. For example, 4 • 23 means 4 • 2 • 2 • 2. Don’t forget that 24 is not 2 • 4. 24 means repeated multiplication of the same factor. 24 = 2• 2 • 2 • 2 = 16, whereas 2 • 4 = 8

Examples Simplify the following exponential expressions by evaluating.

An exponent is a shorthand notation for repeated multiplication.