Understanding Exponents and Coefficients

The video tutorial explains how to solve an equation involving exponents by rewriting and rearranging terms. It guides viewers through the process of solving for variables a and b, using properties of exponents. The solution is verified by substituting back into the original equation, ensuring the correctness of the values found.

What is the initial expression given in the problem?

• 3x^a * Bx^4 = -24x^6

• 3x^a * Bx^4 = 24x^6

• 3x^a * Bx^4 = -24x^5

• 3x^a * Bx^4 = 24x^5

How can the expression 3x^a * Bx^4 be rearranged?

• x^a * 3 * B * x^4

• 3 * B * x^a * x^4

• 3 * x^4 * B * x^a

• B * 3 * x^4 * x^a

What is the result of multiplying x^a and x^4?

• x^(a-4)

• x^(a*4)

• x^(a/4)

• x^(a+4)

What property of exponents is used to combine x^a and x^4?

• Multiply the exponents

• Divide the exponents

• Add the exponents

• Subtract the exponents

What equation is formed by equating the coefficients on both sides?

• B = -24

• 3B = 24

• B = 24

• 3B = -24

What is the value of B after solving the equation 3B = -24?

• 6

• 8

• -8

• -6

What equation is formed by equating the exponents on both sides?

• a + 4 = 6

• a + 4 = 12

• a + 4 = 8

• a + 4 = 10

What is the value of a after solving the equation a + 4 = 6?

• 2

• 6

• 4

• 8

How can you verify the solution for a and B?

• Substitute a = 4 and B = -6 back into the original expression

• Substitute a = 2 and B = -8 back into the original expression

• Substitute a = 8 and B = -2 back into the original expression

• Substitute a = 6 and B = -4 back into the original expression

What is the final expression after substituting the values of a and B?

• 3x^2 * -8x^4 = -24x^6

• 3x^2 * 8x^4 = 24x^6

• 3x^2 * -8x^4 = 24x^6

• 3x^2 * 8x^4 = -24x^6