An exponent is a number that indicates how many times to multiply the base by itself. For example, in $$x^3$$ , 3 is the exponent.

What is the value of $$4^0$$ ?

Any non-zero number raised to the power of 0 is 1. Therefore, $$4^0 = 1$$ .

What is the value of $$x^{-n}$$ ?

$$x^{-n} = \frac{1}{x^n}$$ , where $$x$$ is not equal to 0.

Simplify $$4^{-3}$$ .

$$4^{-3} = \frac{1}{4^3} = \frac{1}{64}$$ .

Evaluate $$y=5\left(\frac{1}{2}\right)^x$$ when x = -2.

When x = -2, $$y = 5\left(\frac{1}{2}\right)^{-2} = 5 * 4 = 20$$ .

What is the exponential form of the equation $$x^a = b$$ ?

The exponential form is $$a = \log_x(b)$$ .

What does it mean for a function to be exponential?

An exponential function is a mathematical function of the form $$f(x) = a * b^x$$ , where $$a$$ is a constant, $$b$$ is a positive real number, and $$b \neq 1$$ .

What is the difference between exponential growth and decay?

Exponential growth occurs when a quantity increases by a constant percentage over time, while exponential decay occurs when it decreases by a constant percentage.

What is the value of $$3^2 * 3^3$$ ?

Using the product rule, $$3^2 * 3^3 = 3^{2+3} = 3^5 = 243$$ .

What is the value of $$x^3 / x^2$$ ?

Using the quotient rule, $$x^3 / x^2 = x^{3-2} = x^1 = x$$ .

If $$a = 2$$ and $$b = 3$$ , what is $$a^b$$ ?

$$a^b = 2^3 = 2 * 2 * 2 = 8$$ .

Exponents and Exponentials Review 12.12.24 Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an exponent?

Back

2.

FLASHCARD QUESTION

Front

What is the base in an exponential expression?

Back

3.

FLASHCARD QUESTION

Front

State the product rule for exponents.

Back

4.

FLASHCARD QUESTION

Front

State the quotient rule for exponents.

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

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