The sat skill exam 5 pdf

Sometimes, you will see an exponent with a vari￾able: bn. The “b” represents a number that will be a fac￾tor to itself “n” times.

Example:

bn where b = 5 and n = 3 Don’t let the variables

fool you. Most

expressions are very

easy once you substi￾tute in numbers.

bn = 53 = 5 × 5 × 5 = 125

Laws of Exponents

■ Any base to the zero power is always 1.

Examples:

50 = 1 700 = 1 29,8740 = 1

■ When multiplying identical bases, you add the

exponents.

Examples:

22 × 24 × 26 = 212 a2 × a3 × a5 = a10

■ When dividing identical bases, you subtract the

exponents.

Examples:

2

2

5

3 = 22

a

a

7

4 = a3

Here is another method of illustrating multipli￾cation and division of exponents:

bm × bn = bm + n

b

b

m

n = bm – n

■ If an exponent appears outside of the parentheses,

you multiply the exponents together.

Examples:

(33)7 = 321 (g4)3 = g12

Squares and Square Roots

The square root of a number is the product of a num￾ber and itself. For example, in the expression 32 = 3 ×

3 = 9, the number 9 is the square of the number 3. If

we reverse the process, we can say that the number 3 is

the square root of the number 9. The symbol for square

root is 25 and it is called the radical. The number

inside of the radical is called the radicand.

Example:

52 = 25; therefore, 25 = 5

Since 25 is the square of 5, we also know that 5 is

the square root of 25.

Perfect Squares

The square root of a number might not be a

whole number. For example, the square root of 7 is

2.645751311 . . . It is not possible to find a whole

number that can be multiplied by itself to equal 7. A

whole number is a perfect square if its square root is

also a whole number.

Examples of perfect squares:

1, 4, 9, 16, 36, 49, 64, 81, 100, . . .

Properties of Square Root Radicals

■ The product of the square roots of two numbers

is the same as the square root of their product.

Example:

a × b = a × b

5 × 3 = 15

■ The quotient of the square roots of two numbers

is the square root of the quotient.

Example:

■ The square of a square root radical is the radicand.

Example:

(N)2 = N

(3)2 = 3 × 3 = 9 = 3

√¯¯¯ √¯¯¯ a

√¯¯¯b

= √¯¯5¯

= a

b (b ≠ 0)

√¯¯¯¯¯ 15

√¯¯¯3

√¯¯¯¯¯ 15

3 =

–THE SAT MATH SECTION–

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