Quiz about Properties of Powers

Question 1

Which relationship expresses the rule for the power of a power?

Accepted Answer

$$\left(a^m\right)^n=a^{m\cdot n}$$

Answer

$$\left(ab\right)^m=a^mb^m$$

Answer

$$a^m\cdot a^n=a^{m+n}$$

Answer

$$\frac{a^m}{a^n}=a^{m-n}\ \ \ \ \left|\ \ a e0 ight|$$

Answer

$$y\ =\ a\cdot b^x$$

Question 2

Which relationship expresses the rule for the power of a product?

Accepted Answer

$$\left(ab\right)^m=a^mb^m$$

Answer

$$\left(a^m\right)^n=a^{m\cdot n}$$

Answer

$$a^m\cdot a^n=a^{m+n}$$

Answer

$$\frac{a^m}{a^n}=a^{m-n}\ \ \ \ \left|\ \ a e0 ight|$$

Answer

$$y\ =\ a\cdot b^x$$

Question 3

Which relationship expresses the rule for the quotient of powers?

Accepted Answer

$$\frac{a^m}{a^n}=a^{m-n}\ \ \ \ \left|\ \ a e0 ight|$$

Answer

$$\left(a^m\right)^n=a^{m\cdot n}$$

Answer

$$\left(ab\right)^m=a^mb^m$$

Answer

$$a^m\cdot a^n=a^{m+n}$$

Answer

$$y\ =\ a\cdot b^x$$

Question 4

Which relationship expresses the rule for the product of powers?

Accepted Answer

$$a^m\cdot a^n=a^{m+n}$$

Answer

$$\left(a^m\right)^n=a^{m\cdot n}$$

Answer

$$\left(ab\right)^m=a^mb^m$$

Answer

$$\frac{a^m}{a^n}=a^{m-n}\ \ \ \ \left|\ \ a e0 ight|$$

Answer

$$y\ =\ a\cdot b^x$$

Question 5

Which relationship is incorrect?

Accepted Answer

$$ab^m=a^mb^m$$

Answer

$$\left(a^m\right)^n=a^{m\cdot n}$$

Answer

$$a^m\cdot a^n=a^{m+n}$$

Answer

$$\frac{a^m}{a^n}=a^{m-n}\ \ \ \ \left|\ \ a e0 ight|$$

Answer

$$y\ =\ a\cdot b^x$$

Question 6

Which relationship is incorrect?

Accepted Answer

$$\frac{a^m}{a^n}=a^{m\div n}\ \ \ \ \left|\ \ a e0 ight|$$

Answer

$$\left(a^m\right)^n=a^{m\cdot n}$$

Answer

$$\left(ab\right)^m=a^mb^m$$

Answer

$$a^m\cdot a^n=a^{m+n}$$

Answer

$$y\ =\ a\cdot b^x$$

Question 7

Which relationship is incorrect?

Accepted Answer

$$\left(a^m\right)^n=a^{m+n}$$

Answer

$$\left(ab\right)^m=a^mb^m$$

Answer

$$a^m\cdot a^n=a^{m+n}$$

Answer

$$\frac{a^m}{a^n}=a^{m-n}\ \ \ \ \left|\ \ a e0 ight|$$

Answer

$$y\ =\ a\cdot b^x$$

Question 8

Which relationship is incorrect?

Accepted Answer

$$a^m\cdot a^n=a^{m\cdot n}$$

Answer

$$\left(a^m\right)^n=a^{m\cdot n}$$

Answer

$$\left(ab\right)^m=a^mb^m$$

Answer

$$\frac{a^m}{a^n}=a^{m-n}\ \ \ \ \left|\ \ a e0 ight|$$

Answer

$$y\ =\ a\cdot b^x$$

Question 9

Select the expression that is equivalent (equal) to $$\left(7^6\right)^4$$ .

Accepted Answer

$$7^{24}$$

Answer

$$7^{10}$$

Answer

$$7^2$$

Answer

$$7^{27}$$

Question 10

What is the correct way to expand $$5^3$$ x $$5^2$$ ?

Accepted Answer

(5x5x5)(5x5)

Answer

(5+5+5)(5+5)

Answer

(5x3)(5x2)

Answer

(5x5)(3x2)

Question 11

Select the expression equivalent (equal) to $$\frac{6^8}{6^3}$$ ?

Accepted Answer

$$6^5$$

Answer

$$6^{11}$$

Answer

$$6^{24}$$

Answer

$$6^{-5}$$

Question 12

Which expression is equivalent (equal) to $$4^{12}$$ x $$7^{12}$$ ?

Accepted Answer

$$28^{12}$$

Answer

$$28^{24}$$

Answer

$$21^{12}$$

Answer

$$28^{144}$$

Question 13

Simplify ( $$x^8$$ )( $$x^{-5}$$ )

Accepted Answer

$$x^3$$

Answer

$$x^{-40}$$

Answer

$$x^{-13}$$

Answer

$$x^{13}$$

Question 14

Simplify the expression using the properties of exponents.

$$\frac{t^{12}}{t^2}$$

Accepted Answer

$$t^{10}$$

Answer

$$t^{14}$$

Answer

$$t^{24}$$

Answer

$$t^6$$

Question 15

$$4^3$$ x $$4^3$$

Accepted Answer

$$4^6$$

Answer

$$4^9$$

Answer

$$16^6$$

Answer

$$16^9$$

Question 16

What is the exponent form for 6?

Accepted Answer

$$6^1$$

Answer

$$6^0$$

Answer

6 x 1

Answer

0

Question 17

What is another way to write $$\frac{6\ x\ 6\ x\ 6}{6\ x\ 6\ x\ 6\ x\ 6\ x\ 6}$$ ?

Accepted Answer

$$\frac{1}{36}$$

Answer

36

Answer

$$\frac{1}{12}$$

Answer

-12

Question 18

What is another way to write $$4^3$$ x $$6^3$$ ?

Accepted Answer

$$\left(4 imes6 ight)^3$$

Answer

24

Answer

4 x 6 x 3

Answer

$$10^3$$

Question 19

What is another way to write $$\frac{1}{5^{-7}}$$ ?

Accepted Answer

$$5^7$$

Answer

$$\frac{1}{35}$$

Answer

$$\frac{1}{-2}$$

Answer

-35

Question 20

In the expression $$x^y$$ , what is x?

Accepted Answer

base

Answer

power

Answer

exponent

Answer

exponential

Answer

quotient

Question 21

In the expression $$x^y$$ , what is y?

Accepted Answer

exponent

Answer

power

Answer

base

Answer

exponential

Answer

quotient

Question 22

What is an expression such as $$x^2$$ called?

Accepted Answer

power

Answer

base

Answer

exponent

Answer

exponential

Answer

product

Question 23

What is an expression such as $$2^x$$ called?

Accepted Answer

exponential

Answer

power

Answer

base

Answer

exponent

Answer

product

Properties of Powers

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