Understanding Exponents and Solving Equations

The video tutorial explains how to solve the equation 2^(5x) = √2 by converting the square root into a rational exponent. It demonstrates that both sides of the equation can be expressed with the same base, allowing the exponents to be equated. The tutorial then shows how to solve for x by manipulating the equation, ultimately finding that x equals one-tenth.

What is the rational exponent form of the square root of 2?

• 2 to the power of 2

• 2 to the power of 3/2

• 2 to the power of 1/2

• 2 to the power of 1

When the bases are the same, what can be said about the exponents?

• They must be different

• They must be equal

• They must be negative

• They must be positive

What equation do we get when we equate the exponents in this problem?

• 5x equals 2

• 5x equals 0

• 5x equals 1

• 5x equals 1/2

What operation is performed to isolate x in the equation 5x equals 1/2?

• Add 5 to both sides

• Subtract 5 from both sides

• Multiply both sides by 1/5

• Divide both sides by 1/2

What is the final solution for x in the equation 5x equals 1/2?

• x equals 5

• x equals 1/2

• x equals 1/5

• x equals 1/10