Exponents |
Multiplying and dividing exponents
Multiplying
Power of power: if a number with an exponent is within parenthesis and has an exponent on the outside then you multiply the exponents and depending on the question asked you simplify
Ex. (a^b)^c equals a^bc
Ex. (6^2)^3 equals 6^6
Product of a power: if there is a number with a exponent being multiplied by a number with the same base and different exponent then you and the exponents
Ex. a^b*a^f equals a^bf
Ex.4^2*4^7 equals 4^9
Power of a product: when there are 2 numbers in parenthesis (it might have more than 2 bases and even an exponent) and an exponent on the outside you distribute the exponent to all bases and exponents
Ex. (a*g^2)^2 equals a^2*g^4
Ex.(2*4^2)^2 equals 2^2*4^4
Dividing
Quotient of powers: when you divide 2 numbers with the same base you subtract the exponents
Ex. a^6/a^4 equals a^2
Ex.2^6/2^4 equals 2^2
Power of a quotient: when you have 2 numbers with parenthesis and and exponent on the outside you distribute the exponent to the numbers then subtract
Power of power: if a number with an exponent is within parenthesis and has an exponent on the outside then you multiply the exponents and depending on the question asked you simplify
Ex. (a^b)^c equals a^bc
Ex. (6^2)^3 equals 6^6
Product of a power: if there is a number with a exponent being multiplied by a number with the same base and different exponent then you and the exponents
Ex. a^b*a^f equals a^bf
Ex.4^2*4^7 equals 4^9
Power of a product: when there are 2 numbers in parenthesis (it might have more than 2 bases and even an exponent) and an exponent on the outside you distribute the exponent to all bases and exponents
Ex. (a*g^2)^2 equals a^2*g^4
Ex.(2*4^2)^2 equals 2^2*4^4
Dividing
Quotient of powers: when you divide 2 numbers with the same base you subtract the exponents
Ex. a^6/a^4 equals a^2
Ex.2^6/2^4 equals 2^2
Power of a quotient: when you have 2 numbers with parenthesis and and exponent on the outside you distribute the exponent to the numbers then subtract