$$4 \times 3^2$ \times 2 = 72$$

$$2 \times (-2)^2$ - (-2) = 10$$

Question 1

Given the expression $$4x^2$$, which of the following correctly identifies the base and the exponent?

Accepted Answer

The base is $$x$$, and the exponent is $$2.$$

Question 2

Which of the following expressions represents 'the square of a number $$y$$ increased by 7'?

Accepted Answer

$$y^2 + 7$

Question 3

If $$a = 3$$ and $$b = 2$$, what is the value of $$4a^2b$?

Accepted Answer

$$4 	imes 3^2$ 	imes 2 = 72$$

Question 4

Which of the following is equivalent to $$5x^3$$ \cdot $$2x^2$$?

Accepted Answer

$$10x^5$$

Question 5

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

Accepted Answer

$$27x^6$$

Question 6

Which of the following best describes the exponent in the expression $$7y^4$$?

Accepted Answer

It tells how many times $$y is $$multiplied by itself.

Question 7

Which of the following is the correct expansion of $$(x + 2)^2$?

Accepted Answer

$$x^2 + 4x + 4$

Question 8

A population of bacteria triples every hour. If the initial population is $$P$$, which expression represents the population after $$t$$ hours?

Accepted Answer

$$P \cdot 3^t$$

Question 9

Which of the following is the correct simplification of $$2x^2$$ + $$3x^2$$?

Accepted Answer

$$5x^2$$

Question 10

If $$f(x) = x^2$ - 4x + 7$$, what is $$f(3)$$?

Accepted Answer

$$3^2 - 4$$ 	imes 3 + 7 = 2$$

Question 11

Which of the following expressions is equivalent to $$x^0$$ for any nonzero $$x$$?

Accepted Answer

$$1$$

Question 12

A car's value depreciates by half each year. If the initial value is $$V$$, what is the value after $$n$$ years?

Accepted Answer

$$V \cdot (\frac{1}{2})^n$$

Question 13

Which of the following is the correct simplification of $$x^3$$ \cdot $$x^4$$?

Accepted Answer

$$x^7$$

Question 14

Which of the following is the correct simplification of $$\frac{x^5$}{x^2$}$$ for $$x 
eq 0$$?

Accepted Answer

$$x^3$$

Question 15

If $$g(x) = 2x^2$ - x$$, what is $$g(-2)$$?

Accepted Answer

$$2 	imes (-2)^2$ - (-2) = 10$$

Understanding Bases and Exponents in Algebraic Expressions

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