Exponents
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Any number that can be expressed as a fraction.
Rational Number

Any positive or negative nonrepeating or nonterminating decimal that cannot be written as a fraction.
Irrational

Rational or Irrational?
1.0005
Rational

Rational or Irrational?
2/5
Rational

Rational or Irrational?
Square root of 34
 Irrational.
 The square root of 34 is not a perfect square.

Rational or Irrational?
3.14259....
 Irrational
 Does not repeat or terminate

Rewrite using exponents
11 x 11 x 11 x 11 x 11 =
11^{5}

Express with an exponent.
16
2^{4} or 4^{2}

Add or subtract.
2x^{2} + 5x^{2}=
7x^{2}

Add or subtract.
k + 2k =
k

7v^{3} + 10v^{3} =
3v^{3}

(2^{3})^{2}=
 2^{3x2} = 2^{6}
 If a power is raised to another power, multiply the exponents together and keep the base the same.

2^{4} x 2^{5} =
 2^{4+5} = 2^{9}
 To multiply two expressions with the same base, add the exponents together and keep the base the same.

(4a)^{2} =
 4^{2}a^{2} = 16a^{2}
 If a product in parentheses is raised to a power, then each factor is raised to the power when parentheses are eliminated.

(3b^{2})^{3} =
3^{3}b^{6} = 27b^{6}

What number makes the statment true?
x^{5}x^{?} = x^{11}
x^{6}

What number makes the statement true?
(y^{?})^{2} = y^{8}
y^{4}

Reduce the expression to simplest form.
5x^{4} =
 5/x^{4}
 Negative exponent indicate reciprocals, not negative numbers. Take the x value in the numerator, which has a negative expnent, to the denominator and change the sign.

(5a)^{2} =
5^{2}a^{2} = 1/5^{2}a^{2} = 1/25a^{2}

(2/3)^{2} =
2^{2}/3^{2} = 4/9