Algebra

Question 1

a^0=

Answer 1

1

Question 2

a^-1=

Answer 2

1/a

Question 3

a^1=

Answer 3

a

Question 4

Exponents: What is the rule for multiplying numbers with the same base?

Ex: 4^3 • 4^5 = ?

Answer 4

If numbers share the same base, their exponents can be added.
Ex: 4^3 • 4^5 = 4^(3+5) = 4^8
Ex: a^m • a^n = a^(m+n)

Question 5

Exponents: what are the rules for dividing numbers with the same base?

Ex: 4^5 / 4^3 = ?

Answer 5

If numbers share the same base, their exponents can be subtracted.
Ex: 4^5 / 4^3 = 4^(5-3) = 4^2
Ex: a^m / a^n = a^(m-n)

Question 6

Exponents: How do you raise an exponent to an exponent?

Ex: (4^3)^5 = ?

Answer 6

If numbers share the same base, their exponents can be multiplied.
Ex: (4^3)^5 = 4^(3•5) = 4^15
Ex: (a^m)^n = a^(m•n) = a^(m•n)

Question 7

Exponents: How do you raise a product (numbers being multiples) to a power?

Ex: (5 • 2)^3 = ?

Ex: (ab)^n = ?

Answer 7

If integers are given, multiply values within the backers first, then raise to the exponent.

Ex: (5 • 2)^3 = 10^3 = 1,000

If variables are given, express as each individual variable raised to that exponent.

Ex: (ab)^n = (a^n)(b^n)

Question 8

a^m / a^n = ?

Answer 8

a^m / a^n = a^(m-n), where a does not equal 0.

Question 9

(a^m)^n = ?

Answer 9

(a^m)^n = a^(m•n)

Question 10

a^m • a^n = ?

Answer 10

a^m • a^n = a^(m+n)

Question 11

(a / b) ^n = ?

Answer 11

(a / b)^n = a^n / b^n

Question 12

How do you calculate the “area” of a rectangle?

Answer 12

Length • Height = Area of a rectangle

Question 13

How do you calculate the area of a triangle?

Answer 13

(Length • Height) / 2 = Area of a triangle

Question 14

How do you calculate he area of a circle?

Answer 14

A = (pi)r^2

Area of a circle = pi • (radius squared)