Lesson Menu Main Idea and New Vocabulary NGSSS Key Concept:Product of Powers Example 1:Multiply...

Main Idea and New VocabularyNGSSSKey Concept: Product of Powers Example 1:Multiply PowersExample 2: Multiply PowersExample 3: Multiply PowersKey Concept: Quotient of PowersExample 4: Divide PowersExample 5: Divide PowersExample 6: Real-World ExampleExample 7: Simplify ExpressionsFive-Minute Check

• Simplify real number expressions by multiplying and dividing monomials.

• monomial

MA.8.A.6.3 Simplify real number expressions using the laws of exponents. MA.8.A.6.4 Perform operations on real numbers (including integer exponents, radicals, percents, scientific notation, absolute value, rational numbers, and irrational numbers) using multi-step and real world problems.

Multiply Powers

Simplify 76 • 7. Express using exponents.

76 • 7 = 76 • 71 7 = 71

= 76 + 1 The common base is 7.

= 77 Add the exponents.

Check 76 · 7 = (7 · 7 · 7 7 · 7 · 7) · 7

= 7 · 7 · 7 7 · 7 · 7 · 7

Multiply Powers

Answer: 77

Simplify r4 • r6. Express using exponents.

Multiply Powers

r4 • r6 = r4 + 6 The common base is r.

= r10 Add the exponents.

Answer: r10

A. t4.5

C. t11

D. t18

Simplify t9 • t2. Express using exponents.

Multiply Powers

Simplify –7x2 • 11x4. Express using exponents.

–7x2 • 11x4 = (–7 • 11)(x2 • x4) Commutative and Associative Properties

= (–77)(x2 + 4) The common base is x.

= –77x6 Add the exponents.

Answer: –77x6

A. –8n30

B. –8n11

C. 8n30

Simplify 4n6(–2n 5). Express using exponents.

Divide Powers

= 612 – 2 The common base is 6.

= 610 Simply.

Answer: 610

Simplify . Express using exponents.

C. 815

D. 8–5

Divide Powers

= a14 – 8 The common base is a.

= a6 Simply.

Answer: a6

B. h14

C. h15

D. h20

MEASUREMENT One centimeter is equal to 10 millimeters, and one kilometer is equal to 106

millimeters. How many centimeters are in one kilometer?

10 = 101

= 106 – 1 or 105 Quotient of Powers

Answer: There are 105 centimeters in one kilometer.

A. 103 times greater

B. 104 times greater

C. 108 times greater

D. 1012 times greater

MEASUREMENT One metric ton is equal to 106 grams and one hectogram is equal to 102 grams. How many times greater is a metric ton than a hectogram?

Group by common base.

= 21 • 52 • 91 Subtract the exponents.

= 2 • 25 • 9 52 = 25

= 450 Simplify.

Simplify Expressions

Simplify

Answer: 450

A. 144

B. 1,152

C. 1,536

D. 9,116

A. 424

B. 411

D. 4–5

A. –6x7y4z2

B. 6x6y4z2

C. 6x6y4z

D. 6x7y4z2

Simplify (–3x6yz2)(–2xy3). Express using exponents.

B. 9–19

C. 919

D. 984

A. a15b30

B. a8b13

C. a2b10

D. a2b7

A. 1,953,125

B. 6,875

C. 555,555,555

D. 390,625

The population of Bangkok was 55 in 1620. By 1990, it increased 54 times. What was Bangkok’s population in 1990?

Lesson Menu Main Idea and New Vocabulary NGSSS Key Concept:Product of Powers Example 1:Multiply...

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