Understanding Exponents and Square Roots

The video tutorial explains how to solve an equation involving square roots and exponents. It begins by expressing the square root of six as six to the power of one-half and 36 as six squared. The tutorial then demonstrates how to equate the exponents by multiplying them, given that the bases are the same. To clear the fraction, both sides of the equation are multiplied by two, leading to a simplified equation. The square root is then removed by squaring both sides, resulting in a linear equation. Finally, the solution for x is found by further simplification, yielding x equals 16.

How can the square root of six be expressed using exponents?

• As six to the power of two

• As six to the power of one half

• As six to the power of three

• As six to the power of zero

What must be true about the exponents when the bases are the same and the expressions are equal?

• The exponents must be zero

• The exponents must be negative

• The exponents must be equal

• The exponents must be different

What operation is performed to clear the fraction in the equation?

• Subtract two from both sides

• Multiply both sides by two

• Add two to both sides

• Divide both sides by two

After clearing the fraction, what is the next step to solve the equation?

• Add 12 to both sides

• Subtract 12 from both sides

• Square both sides

• Divide both sides by four

What is the final value of x after solving the equation?

• x equals 4

• x equals 8

• x equals 12

• x equals 16