How do you simplify the expression $$(3k^5)(-2k^3)$$ ?

To simplify, multiply the coefficients and add the exponents of the same base: $$(3)(-2) = -6$$ and $$k^{5+3} = k^8$$ . Thus, the simplified expression is $$-6k^8$$ .

What does the expression $$(2a)^{-4}$$ simplify to?

Using the property of exponents, $$(2a)^{-4} = \frac{1}{(2a)^4} = \frac{1}{16a^4}$$ .

What is the definition of a geometric sequence?

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

How do you find the value of $$a_n$$ in the sequence defined by $$a_n = 54igg(\frac{1}{3}igg)^{n-1}$$ ?

To find $$a_n$$ , substitute the desired value of $$n$$ into the formula. For example, for $$n=3$$ , $$a_3 = 54igg(\frac{1}{3}igg)^{2} = 54 \times \frac{1}{9} = 6$$ .

What is the difference between linear and exponential functions?

Linear functions have a constant rate of change and are represented by a straight line, while exponential functions grow or decay at a rate proportional to their current value, resulting in a curve.

What is the value of $$\frac{16}{a^4}$$ when $$a = 2$$ ?

Substituting $$a = 2$$ gives $$\frac{16}{(2)^4} = \frac{16}{16} = 1$$ .

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

Multiply the coefficients and add the exponents: $$(-3)(4) = -12$$ and $$x^{2+3} = x^5$$ . Thus, the simplified expression is $$-12x^5$$ .

What is the formula for the sum of the first n terms of an arithmetic sequence?

The sum of the first n terms is given by $$S_n = \frac{n}{2}(a_1 + a_n)$$ , where $$a_n$$ is the nth term.

What is the value of $$\frac{1}{16a^4}$$ when $$a = 4$$ ?

Substituting $$a = 4$$ gives $$\frac{1}{16(4)^4} = \frac{1}{16 \times 256} = \frac{1}{4096}$$ .

Exponents and Exponential Functions MC Review Flashcards

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14 questions

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1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

What is the general formula for the nth term of a geometric sequence?

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What is the formula for the nth term of an arithmetic sequence?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the common ratio in the sequence 54, 18, 6, ...?

Back

7.

FLASHCARD QUESTION

Front

What is the value of the 14th term in the arithmetic sequence where the first term is 6 and the common difference is 5?

Back

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