Understanding Exponents and Roots

The video tutorial explains how to solve an equation involving exponents. It starts with the equation 3 to the power of 'a' equals the fifth root of 3 squared. The tutorial guides viewers through the process of solving for 'a' by using exponent properties, such as raising both sides of the equation to the fifth power. It demonstrates how to simplify the equation using exponent rules and solve for 'a', which equals 2/5. The video also explains the concept of rational exponents and how they relate to roots, providing a deeper understanding of exponentiation.

What is the initial equation given in the problem?

• 3 to the a power equals the fifth root of 3 squared

• 3 to the a power equals 3 squared

• 3 to the a power equals 3 to the fifth power

• 3 to the a power equals the square root of 3

What is the purpose of raising both sides of the equation to the fifth power?

• To eliminate the fifth root

• To solve for a

• To simplify the equation

• To change the base

What is the result of raising 3 to the a power to the fifth power?

• 3 to the 10a power

• 3 to the 2a power

• 3 to the a power

• 3 to the 5a power

What equation do we get after equating the exponents on both sides?

• 5a equals 2

• a equals 5

• 5a equals 3

• a equals 2

What is the value of a after solving the equation?

• 2/5

• 5/2

• 1/5

• 2

What does the result a = 2/5 demonstrate about rational exponents?

• It shows that roots are unnecessary

• It shows that exponents are always integers

• It shows that exponents are always fractions

• It shows the relationship between roots and exponents

How can 3 to the 2/5 power be expressed using roots?

• 3 squared

• 3 to the fifth root

• The square root of 3 to the fifth

• The fifth root of 3 squared

What does the denominator in the exponent 2/5 represent?

• The coefficient

• The power

• The base

• The root

What is the equivalent expression for 3 squared raised to the 1/5 power?

• 3 to the 5/2 power

• 3 to the 1/5 power

• 3 to the 2 power

• 3 to the 2/5 power

What is the final step in verifying the solution?

• Finding the fifth root of 3 squared

• Multiplying the exponents

• Squaring the base

• Changing the base