What is the relationship between the bases in the equation $$2^x = 2^5$$ ?

If the bases are the same, set the exponents equal: x = 5.

6.4 - Solving Exponential Equations Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an exponential equation?

Back

An exponential equation is an equation in which a variable appears in the exponent. For example, $2^x = 8$ .

2.

FLASHCARD QUESTION

Front

How do you solve the equation $2^{-2n} = 2^{6}$ ?

Back

Set the exponents equal: -2n = 6. Solve for n: n = -3.

3.

FLASHCARD QUESTION

Front

What does $a^0 = 1$ mean for any non-zero number a?

Back

Any non-zero number raised to the power of zero equals one.

4.

FLASHCARD QUESTION

Front

Identify the base and exponent in $4^2 = 16$ .

Back

Base: 4, Exponent: 2.

5.

FLASHCARD QUESTION

Front

What is the first step in solving $2^x = 2^{3x-4}$ ?

Back

Set the exponents equal: x = 3x - 4.

6.

FLASHCARD QUESTION

Front

What is the solution to $x^2 = 16$ ?

Back

x = 4 or x = -4.

7.

FLASHCARD QUESTION

Front

How can you express the number 8 using exponents?

Back

8 can be expressed as $2^3$ .

8.

FLASHCARD QUESTION

Front

What is the value of $3^{-2}$ ?

Back

$\frac{1}{9}$ .

9.

FLASHCARD QUESTION

Front

What does it mean to have a negative exponent, such as $a^{-n}$ ?

Back

A negative exponent indicates the reciprocal: $a^{-n} = \frac{1}{a^n}$ .

10.

FLASHCARD QUESTION

Front

How do you simplify $\frac{a^m}{a^n}$ ?

Back

Use the property of exponents: $a^{m-n}$ .

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