10.4 Evaluate Expressions That
Contain Exponents
Common Core Standards
7.NS.2. Apply and extend previous understandings of multiplication and division
and of fractions to multiply and divide rational numbers.
a. Understand that multiplication is extended from fractions to rational numbers by
requiring that operations continue to satisfy the properties of operations,
particularly the distributive property, leading to products such as (–1)(–1) = 1
and the rules for multiplying signed numbers. Interpret products of rational
numbers by describing real-world contexts.
b. Understand that integers can be divided, provided that the divisor is not zero,
and every quotient of integers (with non-zero divisor) is a rational number. If p
and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational
numbers by describing real-world contexts.
c. Apply properties of operations as strategies to multiply and divide rational
numbers.
7.NS.3. Solve real-world and mathematical problems involving the four operations
with rational numbers.
WARM-UP
Evaluate the numerical expressions.
1) 5 × 5
2) 5 2
3) 5 3
Evaluate the variable expressions for x = 4.
4) x gx
5) x
2
6) x 3
Evaluate Expressions That Contain
Exponents
Which should you do first?
+t
−6
×7
p
4
z
2
5
3
NOTES
In a power, the exponent tells you how many times to
multiply the base by itself.
x 3 = x gx gx
Concept Check
Copy the powers then circle the exponent and
underline the base.
y4
(−8)2
− 82
EXAMPLES
Evaluate the numerical expressions.
2
2
11
1
( −10)
5
Evaluate the variable expressions for x = 3 and y = 10.
x2
x
4
y2
y3
EXAMPLES
Evaluate the numerical expressions.
2
(−9)
( −5)3
− 92
NOTES
The steps of Order of Operations:
2) Exponents
3) Divide and Multiply (tiebreaker left to right)
4) Add and Subtract (tiebreaker left to right)
Examples
Evaluate the expressions.
5 × 82
20 ÷ 4 + 23
3g52 + 50 ÷ 2
EXAMPLES
Evaluate the variable expressions for y = 5.
−3y2
Evaluate the variable expressions for p = - 4 and q = 10.
2q2 − p
PRACTICE
Evaluate the numerical expressions.
48 ÷ 23 × 7
100 − 2 × 72 + 81
Evaluate the variable expressions for x = 8
2
2x − 1
x
60 + 10x −
8
2
The number 3 in the following expression is called….
k
3
PRACTICE
Evaluate the expressions for x = - 2.
x
3
x2
−7
2
FINAL QUESTION
Evaluate the variable expressions for x = 9 and y = 12.
2
y
10x 2 +
144