M1 Lab LT 11/12

Front

What does the equation a^m = a^n imply about the values of m and n?

Back

If a^m = a^n, then m = n.

Front

How can you express 64 as a power of 2?

Back

64 can be expressed as 2^6.

Front

What is the solution to the equation 5^{3-2x} = 5^{-x}?

Back

The solution is x = 3.

Front

How do you solve the exponential equation 7^{(x+1)} = 49?

Back

To solve, recognize that 49 = 7^2, so x + 1 = 2, leading to x = 1.

Front

What is the value of x in the equation 5^{-3x - 1} = 25?

Back

The value of x is -1.

Front

What is the definition of an exponential function?

Back

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 x is the variable.

Front

What is the base of an exponential expression?

Back

The base of an exponential expression is the number that is raised to a power.

Front

What is the power in an exponential expression?

Back

The power in an exponential expression indicates how many times the base is multiplied by itself.

Front

What is the property of exponents that states a^m * a^n = a^{m+n}?

Back

This property is known as the Product of Powers Property.

Front

What is the property of exponents that states (a^m)^n = a^{m*n}?

Back

This property is known as the Power of a Power Property.