Powers and Roots: Solving Exponential Equations

The video tutorial explains how to solve a mathematical problem using the laws of indices. In Part A, the problem involves converting 8 into a power of 2 and applying the index law of subtraction to find the value of n. In Part B, the problem requires expanding brackets and using the index law of addition to find the value of k. The tutorial emphasizes the importance of understanding base conversion and the application of index laws to solve such problems effectively.

What is the first step in solving the equation 8 over 2 to the power of 7 equals 2 to the power of n?

• Divide both sides by 8

• Multiply both sides by 2

• Convert 8 into a power of 2

• Add 7 to both sides

How can 8 be expressed as a power of 2?

• 2 to the power of 2

• 2 to the power of 3

• 2 to the power of 4

• 2 to the power of 5

What is the result of subtracting the powers in the expression 2 to the power of 3 divided by 2 to the power of 7?

• 2 to the power of 0

• 2 to the power of -4

• 2 to the power of 4

• 2 to the power of 10

In Part B, what operation is performed on the powers when expanding the brackets in 13 to the power of negative 6 raised to the power of 4?

• Division

• Addition

• Subtraction

• Multiplication

What is the result of multiplying the powers in the expression 13 to the power of negative 6 raised to the power of 4?

• 13 to the power of -24

• 13 to the power of -10

• 13 to the power of 10

• 13 to the power of 24

What is the final value of k in the equation 13 to the power of negative 24 times 13 to the power of 5?

• 29

• 19

• -29

• -19

What index law is applied when multiplying two powers with the same base?

• Divide the powers

• Multiply the powers

• Add the powers

• Subtract the powers