Focus on Expressions and Equations VOCABULARY Lessons 3 – 5

Product of Powers Property The product of powers with the same base is equal to the that base raised to the sum of the exponents. In symbols, am  an = am+n, for any nonzero number a and any integers n and m. Examples: 37 x 34 = 311, p3 x p4 = p7

Power of a Product Property A product raised to a power is equal to the product of factors, each raised to that power. In symbols, (ab)n = anbn, for any nonzero numbers a and b and any integer n. Example: (3b)3 = 33 x b3 = 27b3

Power of a Power Property A power raised to a power is equal to the same base raised to the product of the exponents. In symbols, (am)n = amn, for any nonzero number a and any integers m and n. Example: (44)2 = 44x2 = 48

Quotient of Powers Property The quotient of powers with the same base is equal to that same base raised to the difference of the exponents. In symbols, am an = am-n, for all nonzero numbers a and all integers m and n. Example: ( 9𝑐5 3𝑐1 ) = 3c4

Power of a Quotient Property A quotient raised to a power is equal to the dividend raised to the power divided by the divisor raised to the power. In symbols, ( 𝑎 𝑏 )n = an bn , for any nonzero numbers a and b and any integer n. Example: ( 𝑐 3 )5 = 𝑐5 35 = 𝑐5 243