Solving Equations with Rational Exponents

This video tutorial teaches how to solve equations involving variables with rational exponents. It covers the importance of having the same base to add or subtract exponents and provides examples of solving equations with rational and fractional exponents. The tutorial also explores inverse relationships in exponent equations and the significance of different bases. Key concepts such as cube roots, square roots, and radicals are discussed, emphasizing the need for consistent bases to equate exponents.

What must be true for numbers or variables with exponents to be added or subtracted?

• The coefficients must be zero.

• The bases must be different.

• The exponents must be different.

• Both the bases and exponents must be the same.

In the example where 2 to the 3x equals 2 to the 1, what is the value of x?

• 3/2

• 2/3

• 1/3

• 1/2

When solving 2 to the x over 3 times 2 to the x over 3 times 2 to the x over 3 equals 2, what is the value of x?

• 3

• 1/3

• 1

• 2/3

If 5 to the x equals 5 to the 1/4, what does 5 to the 1/4 represent?

• 5 squared

• The fourth root of 5

• The cube root of 5

• The square root of 5

What must be true to set exponents equal to each other in an equation?

• The bases must be different.

• The exponents must be different.

• The bases must be the same.

• The coefficients must be equal.