Properties and Applications of Exponents

The video tutorial explains how to solve an exponential equation by using properties of negative exponents. It begins with rewriting the equation to simplify it, then proceeds to solve it without using logarithms by expressing the base in terms of a common base. The solution is verified by substituting back into the original equation, ensuring the correctness of the result.

What is the property of negative exponents used to rewrite one divided by nine raised to the power of negative one?

• a^(-m) = -a^m

• a^(-m) = a^m

• a^(-m) = a^(1/m)

• a^(-m) = 1/a^m

How can the equation 81^(x/2) - 4 = 9 be simplified using exponent rules?

• By dividing both sides by 9

• By adding 4 to both sides

• By multiplying both sides by 2

• By rewriting 81 as 9^2

What is the result of raising a power to another power in the equation 9^(2x/2) - 4 = 9?

• Multiply the exponents

• Subtract the exponents

• Add the exponents

• Divide the exponents

When the bases are the same, what must be true about the exponents in the equation 9^(x-8) = 9?

• The exponents must be negative

• The exponents must be equal

• The exponents must be positive

• The exponents must be different

What is the solution for x in the equation x - 8 = 1?

• x = 7

• x = 8

• x = 9

• x = 10

How is the solution verified by substitution in the original equation?

• By checking if both sides equal zero

• By checking if both sides equal nine

• By checking if both sides equal eighty-one

• By checking if both sides equal one

What is the value of 81 raised to the power of nine halves minus four?

• Positive nine

• Zero

• Eighty-one

• Negative nine

What is the simplified form of one divided by nine raised to the power of negative one?

• Zero

• Negative nine

• Nine

• One

What does the verification process confirm about the solution x = 9?

• The solution is incorrect

• The solution is partially correct

• The solution is correct

• The solution needs adjustment

What is the purpose of evaluating both sides of the equation on a calculator?

• To find a new solution

• To change the base

• To simplify the equation

• To verify the solution