Powers: Solving Exponential Equations with Multiple Bases and Variables

The video tutorial explains how to solve a math problem involving indices. It begins by converting all numbers to the same base, specifically base 2, to simplify the expression. The tutorial then demonstrates how to use the laws of indices to combine and simplify terms, ultimately solving for the variable x. The solution is broken down into steps, with explanations of how marks are awarded for each part of the process. Key points include converting numbers to the same base, using the laws of indices, and solving algebraic equations.

What is the first step in solving the equation 128 = 4^(2x) * 2^x?

• Convert 2 to a base of 4

• Convert 4 to a base of 128

• Convert 128 to a base of 2

• Convert 128 to a base of 4

How can the number 4 be expressed as a power of 2?

• 2^3

• 2^4

• 2^2

• 2^1

What is the simplified form of the expression 2^(4x) * 2^x?

• 2^(4x * x)

• 2^(4x / x)

• 2^(4x - x)

• 2^(4x + x)

If 2^7 = 2^(5x), what is the value of x?

• x = 5/7

• x = 7

• x = 5

• x = 7/5

What is the first mark awarded for in this problem?

• Using the law of indices

• Finding the value of x

• Converting 4 to a base of 2

• Setting up the expression with the same base

What is the final answer for x in the problem?

• x = 0.7

• x = 1.4

• x = 5/7

• x = 7/5

What should you remember about multiplying powers with the same base?

• Multiply the exponents

• Subtract the exponents

• Divide the exponents

• Add the exponents