Law of Multiplying and Dividing Indices

Law of Multiplying and Dividing Indices

Poll

What is your confidence level with multiplying and dividing indices?

• Confident I could teach this

• Confident I could get the answer, but not teach it

• With a little help I could answer questions about this

• I would need a lot of help

Multiple Choice

According to exponent rules, when we multiply two powers with the same base we _______ the exponents.

Example: c⁶ ⋅ c⁴

• add

• subtract

• multiply

• divide

Multiple Choice

What is the correct law for multiplication? a^m x aⁿ =

• a^m+n
• a^m + aⁿ
• a^mxn
• a^mn

Multiple Choice

When multiplying terms with the same base, you should...

• Multiply the indices

• Add the indices

• Subtract the indices

• Divide the indices

Multiple Choice

Write in index notation. 2 x 3 x 3 x 5 x 5 x 5 x 2

• 2 x 3² x 5²
• 2² + 3² + 5³
• 2² x 3² x 5³

Multiple Choice

Simplify: x ∙ x ∙ x ∙ x ∙ x ∙ x

(a dot means multiply)

• x⁶

• 6x

• x³

• 6x⁶

Multiple Choice

Solve 5³

• 8
• 15
• 75
• 125

Multiple Choice

a³ x a⁵

• a¹⁵
• a²
• a⁸
• a^-2

Multiple Choice

 $d^4\cdot d^5$  
(a dot means multiply)

• 2d⁴

• d⁹

• d²

• 2d

Multiple Choice

3⁴ ⋅ 3⁷

(a dot means multiply)

• 3²⁸

• 3³

• 3^-3

• 3¹¹

Multiple Choice

Write in index form: $7^2\times7^3=$  

•  $7^5$  

•  $7^6$  

•  $14\times21$  

•  $49^{2\times3}$  

Multiple Choice

Simplify: 4x²y × 9xy²

• 36x³y³
• 36xy³
• 13x²y²
• 13x³y³

Multiple Choice

Simplify: 3x³ × 6x⁸

• 18x¹¹
• 18x²⁴
• 9x¹¹
• 9x²⁴

Multiple Choice

Simplify: 3⁵ x 3⁷

• 3¹²
• 9¹²
• 3³⁵
• 9³⁵

Multiple Choice

Simplify 5b⁴×4b³

• 20b⁷
• 9b⁷
• 9b¹²
• 20b¹²

Multiple Choice

Simplify 3b×6b²

• 9b⁴
• 6b⁵
• 18b³
• 9b³

Multiple Choice

Simplify 5d⁴x3d⁸

• 8d³²

• 15d⁴

• 15d¹²

• 8d¹²

Multiple Choice

Simplify 2b×3b²×5b³

• 30b⁶

• 10b⁶

• 30b⁵

• 30b

Multiple Choice

Simplify: 4x²y × 9xy²

• 36x³y³
• 36xy³
• 13x²y²
• 13x³y³

Multiple Choice

Simplify: (3a²b)² × (2ab)³

• 6a⁷b⁵

• 72a⁷b⁵

• 36a⁵b⁴

• 18a⁴b²

Multiple Choice

What is the area of a rectangle with dimensions listed below:

length = 10x⁷

width = 7x⁵

• 70x¹²

• 70x³⁵

• 17x¹²

• 17x³⁵

Multiple Choice

Billy was asked to solve 3⁵∙3⁴. He got 9²⁰. What error did he make?

• When he multiplies exponents, he is supposed to add the base and the exponent
• When he multiplies exponents, he is supposed to multiply the base and keep the exponents
• When he multiplies exponents, he is supposed to keep the base and add the exponents if the base is the same
• None of the above

Multiple Choice

A quotient is the answer in a _____________ problem.

• addition

• subtraction

• multiplication

• division

Multiple Choice

When a positive integer is divided by a positive integer, the quotient is ____________.

• positive

• negative

• zero

Multiple Choice

According to exponent rules, when we divide powers we _______ the exponents.

• add
• subtract
• multiply
• divide

Multiple Choice

What is the correct law for division? a^m ÷ aⁿ =

• a^m-n
• a^m - aⁿ
• a^m÷n
• a^m/n

Multiple Choice

Write 9⁵ ÷ 9³ as a single power

• 9²
• 9⁸
• 9¹⁵

Multiple Choice

 $x^{12}\div x^4$  

•  $x^8$  

•  $x^4$  

•  $x^3$  

Multiple Choice

Simplify: χ³ ÷ χ²

• χ

• χ⁵

• χ⁶

• χ^-1

• 1/χ

Multiple Choice

c⁵ ÷ c

• 5

• 5c

• c⁴

• c⁵

Multiple Choice

 $\frac{x^4}{x}=$  

•  $\left(x\div1\right)^4$  

•  $x^{\left(4\div1\right)}$  

•  $x^{\left(4-0\right)}$  

•  $x^{\left(4-1\right)}$  

Multiple Choice

Simplify $\frac{x^6}{x^2}$  

•  $x^4$  

•  $x^3$  

•  $x^8$  

Multiple Choice

 $\frac{27x^9}{9x^2}$  

•  $3x^6$  

•  $3x^4$  

•  $18x^6$  

Multiple Choice

Simplify $12x^9\div6x^3$  

•  $2x^6$  

•  $6x^6$  

•  $2x^3$  

Multiple Choice

Simplify  $\frac{9x^2y^5}{3x^3y^2}$  

•  $\frac{3y^3}{x}$  

•  $\frac{6y^3}{x}$  

•  $3xy^3$  

•  $6xy^3$  

Multiple Choice

Evaluate the expression using the quotient rule.

• 2¹⁴ z¹³
• 2²/z⁷
• 2¹⁴/ z⁷
• 2² z⁷

Multiple Choice

Simplify $\frac{x^6y^5}{x^2y^3}$  

•  $x^4y^2$  

•  $x^3y^2$  

•  $x^8y^8$  

Multiple Choice

Simplify $\frac{6x^{15}}{3x^5}$  

•  $2x^{10}$  

•  $3x^3$  

•  $2x^5$  

Multiple Choice

Simplify: 64x¹⁶y¹² ÷ 4x⁸y³

• 60x²y⁴

• 16x²y⁴

• 60x⁸y⁹

• 16x⁸y⁹

Multiple Choice

(-4)⁷ ÷ (-4³) is equivalent to

• (-4)⁴

• 4⁴

• -4⁴

• 4^-4

Multiple Choice

a⁷×a⁴÷a⁵

• a⁷
• a⁶
• a⁴
• a¹¹

Multiple Choice

Write (4⁷ x 4³) ∕  4⁴ as a single power

• 4¹⁴
• 4¹
• 4⁸
• 4⁶

Multiple Choice

Simplify  $k^7\times k^2\div k^5$  

•  $k^4$  

•  $k^9$  

•  $k^{14}$  

•  $k^{19}$  

Multiple Choice

 $\frac{x^7\times x^5}{x^{12}\div x^4}$  

•  $x^4$  

•  $x^3$  

•  $x^5$  

Multiple Choice

 $\frac{x^5\times x^3}{x^2}$  

•  $x^6$  

•  $x^4$  

•  $x^2$  

Multiple Choice

Simplify: (4pq³)² ÷ (2p²q)³

• 2p^-4q³
• 8p⁴q³
• 16p⁴q²
• 4p^-4q²

Poll

What is your confidence level with multiplying and dividing indices?

• Confident I could teach this

• Confident I could get the answer, but not teach it

• With a little help I could answer questions about this

• I would need a lot of help