Understanding and Solving Exponential Equations

In this video, Gis introduces exponential equations, explaining their structure and how to solve them. She demonstrates solving techniques using prime factor decomposition and provides examples with different bases and exponents. The video also covers advanced techniques, including handling fractional exponents and roots, emphasizing the importance of understanding power properties.

What distinguishes an exponential equation from a first-degree equation?

• An exponential equation always has a base of 10.

• The unknown is always a fraction in an exponential equation.

• A first-degree equation has no unknowns.

• The unknown is in the exponent in an exponential equation.

How can you solve an exponential equation with base 2 and a result of 32?

• By adding 2 five times.

• By dividing 32 by 2.

• By decomposing 32 into 2^5.

• By multiplying 2 by 16.

When solving 3^(2x) = 81, what is the equivalent power of 81?

• 3^2

• 3^3

• 3^4

• 3^5

What is the first step in solving an exponential equation involving fractions?

• Decompose both the numerator and denominator into prime factors.

• Add the numerator and denominator.

• Convert the fraction to a decimal.

• Multiply both sides by the denominator.

In the equation 16^(x-3) = 1, what property of exponents is used to simplify the equation?

• The base can be ignored if it is one.

• Any number raised to the power of zero is one.

• The base can be divided by the exponent.

• The exponent can be multiplied by the base.

How do you handle a negative exponent when solving an exponential equation?

• Add the exponent to the base.

• Invert the base and change the sign of the exponent.

• Ignore the negative sign.

• Multiply the exponent by negative one.

What is the result of 2^(-5/2) in terms of base 2?

• 1/2^5

• 2^5

• 1/2^(-5)

• 2^(-5)

How can you express the fourth root of 343 using a fractional exponent?

• 343^(3/4)

• 343^(1/4)

• 343^(4/3)

• 343^(1/3)

What is the first step in solving an equation with a root and a fractional exponent?

• Divide the root by the exponent.

• Convert the root to a power with a fractional exponent.

• Multiply the root by the exponent.

• Add the root to the exponent.

What is the value of x in the equation 7^(2x+2) = 343^(3/4)?

• x = 5/8

• x = -5/8

• x = 3/4

• x = -3/4