Understanding Exponential Equations

The video tutorial explains how to solve equations using like bases. It covers two examples: one using base 5 and another using base 4. The tutorial demonstrates the application of the negative exponent property and how to equate exponents when the bases are the same. It also includes step-by-step solutions to linear equations derived from the initial exponential equations.

What is the main idea behind solving equations using like bases?

• To set the exponents equal once the bases are the same.

• To convert all numbers to base 10.

• To eliminate all exponents from the equation.

• To make both sides of the equation equal to zero.

In the first example, what property is used to rewrite 1/5 as 5^-1?

• Negative exponent property

• Positive exponent property

• Zero exponent property

• Fraction exponent property

What happens to the exponent when a term moves across a fraction bar?

• It becomes zero.

• It remains unchanged.

• It changes sign.

• It doubles.

What is the result of distributing -1 in the equation -1 * (x + 4)?

• x - 4

• -x - 4

• x + 4

• -x + 4

What is the final solution for x in the first example?

• 5/14

• 14/5

• -14/5

• -5/14

In the second example, why is 1/16 rewritten as 4^-2?

• Because 16 is the fourth power of 4.

• Because 16 is the square root of 4.

• Because 16 is the square of 4.

• Because 16 is the cube of 4.

What is the base used in the second example?

• Base 3

• Base 4

• Base 5

• Base 2

What is the simplified form of the equation -4x + 6 = 2x - 2 after moving terms?

• 6x = 8

• 2x = 6

• 8x = 6

• 4x = 8

What is the final solution for x in the second example?

• 4/3

• 3/4

• 3/2

• 2/3

What is the purpose of multiplying exponents when powers are raised to powers?

• To decrease the exponent value.

• To increase the exponent value.

• To eliminate the base.

• To simplify the equation.