Exploring Adding and Subtracting Rational Expressions

This video tutorial covers solving exponential equations by using properties of exponents. It explains the steps to simplify each side of the equation, rewrite them to have the same base, and set the exponents equal to each other. The tutorial includes examples with both common and different bases, demonstrating how to solve for variables and check solutions.

What is the first step in solving exponential equations?

• Rewrite the equation with a common base

• Substitute values to check the solution

• Simplify each side using properties of exponents

• Set the exponents equal to each other

In the equation 2^(x+1) = 2^9, what is the value of x?

• 7

• 10

• 9

• 8

If both sides of an equation already have the same base, what should you do next?

• Multiply the bases

• Change the base of the equation

• Set the exponents equal to each other

• Simplify using properties of exponents

For the equation 3^(2k+2) = 3^(5k-1), what is the value of k?

• 3

• 1

• 2

• 4

How can you solve an equation where the bases are not initially the same?

• Add the exponents directly

• Subtract one base from the other

• Divide the exponents

• Rewrite one or both bases to make them common

When solving 10^(-4+9) = 10^(3v-7), what does v equal?

• 4

• 5

• 3

• 6

What is a crucial step after solving the equation for the variable?

• Simplify the base

• Set the equation to zero

• Substitute the solution back into the original equation to check

• Rewrite the equation

If 4^(3x) = 8^(x-1), what is the value of x after simplifying the bases?

• -1

• 0

• 1

• 2

What should you do if the equation involves complex bases like 125 and 25?

• Rewrite both numbers with a common base

• Approximate the bases

• Ignore the bases and focus on exponents

• Divide the larger base by the smaller base

What is the solution for x in the equation 125^(y) = 25, after rewriting the bases?

• One-half

• Three-fourths

• One-third

• Two-thirds