Quiz about Index Laws Quiz

Question 1

Simplify the expression $$x^{-3}$$ .

Accepted Answer

$$\frac{1}{x^3}$$

Answer

$$\frac{1}{3x}$$

Question 2

What is the result of $$(x^3)(x^4)$$ ?

Accepted Answer

$$x^7$$

Answer

$$x$$

Question 3

Simplify the expression $$\frac{x^5}{x^2}$$ .

Accepted Answer

$$x^3$$

Answer

$$x^{10}$$

Question 4

What is the value of $$x^0$$ for any non-zero $$x$$ ?

Accepted Answer

$$1$$

Answer

$$x$$

Question 5

Simplify the expression $$(x^3)^4$$ .

Accepted Answer

$$x^{12}$$

Answer

$$x^{3/4}$$

Question 6

Simplify the expression $$(2x^3)^2$$ .

Accepted Answer

$$4x^6$$

Answer

$$2x^6$$

Question 7

What is the simplified form of $$x^{-2}y^{-3}$$ ?

Accepted Answer

$$\frac{1}{x^2y^3}$$

Answer

$$\frac{y^3}{x^2}$$

Question 8

Simplify the expression $$\frac{x^4}{x^{-3}}$$ .

Accepted Answer

$$x^7$$

Answer

$$x$$

Question 9

What is the result of $$(xy)^3$$ ?

Accepted Answer

$$x^3y^3$$

Answer

$$x^3 + y^3$$

Question 10

Simplify the expression $$(2x^2y)^3$$ .

Accepted Answer

$$8x^6y^3$$

Answer

$$6x^5y^3$$

Question 11

What is the result of $$(3x)^2$$ ?

Accepted Answer

$$9x^2$$

Answer

$$3x^2$$

Question 12

Simplify $$\frac{2x^3y^2}{4xy}$$ .

Accepted Answer

$$\frac{1}{2}x^2y$$

Answer

$$2x^2y$$

Question 13

What is the simplified form of $$(3x^2)^3$$ ?

Accepted Answer

$$27x^6$$

Answer

$$27x^5$$

Question 14

Simplify the expression $$\frac{3x^4}{9x^2}$$ .

Accepted Answer

$$x^2$$

Answer

$$3x^2$$

Question 15

What is the result of $$(x^2y)^2$$ ?

Accepted Answer

$$x^4y^4$$

Answer

$$x^2y^2$$

Question 16

Simplify the expression $$(3x^3y)^2$$ .

Accepted Answer

$$9x^6y^2$$

Answer

$$9x^5y^2$$

Question 17

What is the simplified form of $$\frac{4x^2}{2x}$$ ?

Accepted Answer

$$2x$$

Answer

$$2x^2$$

Question 18

What is the result of $$(2xy)^4$$ ?

Accepted Answer

$$16x^4y^4$$

Answer

$$16xy$$

Question 19

What is the result of $$(5x^3)^2$$ ?

Accepted Answer

$$25x^6$$

Answer

$$10x^3$$

Question 20

Simplify the expression $$\frac{8x^5}{2x^2}$$ .

Accepted Answer

$$4x^3$$

Answer

$$x^3$$

Question 21

What is the simplified form of $$(2x^2y^3)^3$$ ?

Accepted Answer

$$8x^6y^9$$

Answer

$$2x^6y^9$$

Question 22

What is the simplified form of $$(4x^3)^2$$ ?

Accepted Answer

$$16x^6$$

Answer

$$16x^5$$

Question 23

Simplify the expression $$\frac{x^6}{x^3}$$ .

Accepted Answer

$$x^3$$

Answer

$$x^9$$

Question 24

What is the result of $$(2x^2)^3$$ ?

Accepted Answer

$$8x^6$$

Answer

$$8x^5$$

Question 25

Simplify the expression $$\frac{5x^7}{x^2}$$ .

Accepted Answer

$$5x^5$$

Answer

$$\frac{5}{x^5}$$

Question 26

What is the result of $$(3x^2y)^3$$ ?

Accepted Answer

$$27x^6y^3$$

Answer

$$9x^6y^3$$

Question 27

What is the simplified form of $$x^4 \cdot x^{-1}$$ ?

Accepted Answer

$$x^3$$

Answer

$$x^5$$

Question 28

What is the result of $$(4x^3)^2$$ ?

Accepted Answer

$$16x^6$$

Answer

$$16x^5$$

Question 29

Simplify the expression $$\frac{2x^8}{x^3}$$ .

Accepted Answer

$$2x^5$$

Answer

$$2x^{11}$$

Question 30

What is the simplified form of $$x^3 \cdot x^2$$ ?

Accepted Answer

$$x^5$$

Answer

$$x^6$$

Question 31

What is the result of $$(4x^3)^2$$ ?

Accepted Answer

$$16x^6$$

Answer

$$8x^6$$

Question 32

Simplify the expression $$\frac{3x^4}{x^2}$$ .

Accepted Answer

$$3x^2$$

Answer

$$x^2$$

Question 33

What is the simplified form of $$(x^2y^2)^3$$ ?

Accepted Answer

$$x^6y^6$$

Answer

$$x^6y^3$$

Question 34

What is the result of $$(5x^3y)^2$$ ?

Accepted Answer

$$25x^6y^2$$

Answer

$$10x^3y^2$$

Question 35

Simplify the expression $$\frac{9x^9}{3x^3}$$ .

Accepted Answer

$$3x^6$$

Answer

$$3x^3$$

Question 36

What is the simplified form of $$(3x^2y^2)^4$$ ?

Accepted Answer

$$81x^8y^8$$

Answer

$$81x^6y^6$$

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