Product of Powers
Quotient of Powers
Negative & Zero Powers
Scientific & Standard Notation
Exponents
100
Simplify the expression. Write your answer as a power.
810 • 84
814
Keep the base and add the exponents 810 + 4 = 814100
Simplify the expression. Write your answer as a power.
y^9/y^7
y^2
Keep the base, subtract the denominator exponent from the numerator exponent (y9 - 7 = y2).
100
Evaluate the expression:
1580
1 - Any number to the 0 power (other than 0) is equal to 1.
100
Write the number in scientific notation.
750
7.5 x 102
Place the decimal point to the right of the lead digit and between the 7 and 5. The decimal moved two spaces and as a result of the large number 750, the exponent is positive.
100
Write the product using exponents.
11 • 11 • 11 • 11 • 11
115
11 multiplied by itself 5 times. 11 is the base and 5 is the exponent.
200
Simplify the expression. Write your answer as a power.
(qrs)3
g3r3s3
The exponent of 3 is distributed (with multiplication) to each of the three variables inside the parentheses.
Each variable has a hidden 1 exponent next to it.
200
Simplify the expression. Write your answer as a power.
10^12/10^7
105
Keep the base, subtract the denominator exponent from the numerator exponent (1012 - 7 = 105).
200
Evaluate the expression.
44 • 4-4
40 = 1
Keep the base of four and add the exponents 44 + (-4) = 40. Any number to the zero power (other than zero) is equal to 1.
200
Write the number in standard form.
1.66 x 109
1,660,000,000
You have a positive power of ten so your number will be getting larger (decimal moves to the right 9 spaces). Add zeros above any jump with no number to get 1660000000 or 1,660,000,000.
200
Write the product using exponents.
a • a • a
a3
a multiplied by itself 3 times (a3).
300
Simplify the expression. Write your answer as a power.
c3 • c2 • c4
c9
Keep the base of c and add all three exponents c3 + 2 + 4 = c9.
300
Simplify the expression. Write your answer as a power.
8^9/8^7
82
Keep the base of 8 and subtract the denominator exponent from the numerator exponent. 89 - 7 = 82
300
Simplify the expression.
g^-9/h^-3
h^3/g^9
Move both variables as their positive reciprocal (flip them and make the exponent positive).
300
Write 3.876 x 107 in standard form.
38,760,000
You have a positive power of ten so your number will be getting larger (decimal moves to the right 7 spaces). Add zeros above any jump with no number to get 38760000 or 38,760,000.
300
Write the product using exponents.
4 • 4 • 4 • 4 • 4 • 4
46
4 multiplied by itself 6 times (46).
400
Simplify the expression. Write your answer as a power.
(c2d4)4
c8d16
The exponent of 4 is distributed (with multiplication) to each of the two variables inside the parentheses.
For c, multiply 2 x 4 and for d, multiply 4 x 4.
400
Simplify the expression. Write your answer as a power.
a^3/a^2*b^4/b^3
ab
Keep the base of a and subtract the denominator exponent from the numerator exponent. a3 - 2 = a
Keep the base of b and subtract the denominator exponent from the numerator exponent. b4 - 3 = b
Combine the variables to get ab
400
Evaluate the expression.
00
Undefined
Zero to the zero power is undefined.
400
Write 523 x 10-4 in standard form.
0.0523
You have a negative power of ten so your number will be getting smaller (decimal moves to the left 4 spaces). Add zeros above any jump with no number to get .0523 or 0.0523.
400
Write the product using exponents.
2 • 2 • x • x
22x2
2 multiplied by itself 2 times (22).
x multiplied by itself 2 times (x2).
Combine the two parts 22x2
500
Simplify the expression. Write your answer as a power.
76
Keep the base of 7 and add the exponents in the numerator 75 + 3 = 78.
Subtract the exponent in the denominator from the exponent in the numerator 78 - 2 = 76
500
Simplify the expression while using only positive exponents.
4/x^6
Divide 8 by 2 = 4.
Subtract denominator exponent from numerator exponent x3 - 9 = x-6.
Bring x-6 down to the denominator as its positive reciprocal x6.
500
Simplify the expression by writing with only positive exponents.
9c^7
Move only the c-4 up as a positive reciprocal (c4). Add the exponents c3 + 4 to get 9c7.
500
Write the number in scientific notation.
0.00000000009831
9.831 x 10-11
The decimal moves 11 places to the right between the 9 and 8. The example is a very small number so your exponent is negative.
500
Write the product using exponents.
(-6) • (-6) • (-6) • z • z
(-63)z2
(-6) multiplied by itself 3 times (-63).
z multiplied by itself 2 times (z2).
Combine the two parts (-63)z2