Solving Exponential and Linear Equations

The video tutorial explains how to solve an equation involving exponents with different bases. It begins by introducing the problem and the importance of having the same base for exponents. The instructor then demonstrates how to rewrite a fraction as a whole number with a negative exponent. Using power rules, the equation is simplified to have the same base, allowing the exponents to be set equal. The solution is found by applying algebraic methods, and the tutorial concludes with a recap of the key steps and concepts.

Why is it important to have the same base when dealing with exponents?

• To simplify the calculation

• To ensure the exponents are equal

• To make the equation more complex

• To avoid using negative numbers

What is the equivalent of x to the negative m?

• 1 over x to the m

• x to the m times n

• x to the n

• x to the m

How can 1 over x to the n be rewritten using negative exponents?

• x to the negative n

• x to the n times m

• x to the n

• 1 over x to the negative n

What is the first step in rewriting the problem to have the same base?

• Multiply the exponents

• Convert all numbers to fractions

• Rewrite 1 over 9 as 9 to the negative first power

• Use the power of a power rule

How can 9 be rewritten to have a base of 3?

• 3 squared

• 3 cubed

• 3 to the first power

• 3 to the negative second power

What does the power of a power rule state?

• x to the m times n equals x to the m plus n

• x to the m raised to the n equals x to the m times n

• x to the m divided by n equals x to the m minus n

• x to the m plus n equals x to the m times n

What is the result of applying the power of a power rule to 3 squared raised to the negative first?

• 3 to the second

• 3 to the first

• 3 to the negative second

• 3 to the zero

What is the significance of the power of a power rule in this problem?

• It simplifies the multiplication of exponents

• It is not used in this problem

• It allows for the addition of exponents

• It helps in rewriting the bases to be the same

What is the equivalent of 3 squared raised to the negative first power?

• 3 to the negative second

• 3 to the first

• 3 to the second

• 3 to the zero

What is the next step after rewriting the bases to be the same?

• Equate the exponents

• Subtract the exponents

• Multiply the exponents

• Add the exponents