CA #4 Review #2

Front

What is the property of exponents that states \( a^{-n} = \frac{1}{a^n} \)?

Back

This property allows us to rewrite negative exponents as fractions.

Front

Solve: \( 7^{-x} = 49 \)

Back

\( x = -2 \)

Front

What is the definition of an exponential equation?

Back

An exponential equation is an equation in which a variable appears in the exponent.

Front

Solve for n: \( 2^{-2n} = 2^{6} \)

Back

\( n = -3 \)

Front

What is the base of an exponential function?

Back

The base is the constant value that is raised to a power, such as 2 in \( 2^x \).

Front

Solve for x: \( 2^{x+6} = 2^{5} \)

Back

\( x = -1 \)

Front

What is the rule for solving exponential equations with the same base?

Back

If \( a^m = a^n \), then \( m = n \).

Front

Solve: \( 3^{3} = 3^{4x + 2} \)

Back

\( x = \frac{1}{4} \)

Front

What does it mean to isolate the variable in an equation?

Back

To isolate the variable means to manipulate the equation so that the variable is on one side and all other terms are on the opposite side.

Front

Solve for m: \( 2^{-m} = 2^{3m-3} \)

Back

\( m = \frac{3}{4} \)