GCSE Secondary Maths Age 13-17 - Algebra: Indices - Explained

The video tutorial addresses a mathematical problem involving indices, specifically solving for x in the equation 16^(1/5) * 2^x = 8^(3/4). The instructor explains the process of converting numbers to powers of 2 to simplify the equation, demonstrating the multiplication of indices. The solution involves rewriting the equation in terms of powers of 2, simplifying, and solving for x, which results in x = 1.45. The tutorial also discusses the allocation of marks for the problem and emphasizes the importance of recognizing patterns in numbers to find efficient solutions.

What is the first step in solving the problem involving indices?

• Use a calculator to find the answer directly.

• Convert all numbers to powers of 2.

• Add all the indices together.

• Multiply all the numbers together.

How do you simplify 16 to the power of 1/5?

• By converting it to 2 to the power of 4/5.

• By converting it to 2 to the power of 1/5.

• By converting it to 2 to the power of 3/5.

• By converting it to 2 to the power of 5/4.

What is the result of raising 8 to the power of 3/4?

• 2 to the power of 12/4

• 2 to the power of 6/4

• 2 to the power of 9/4

• 2 to the power of 3/4

What equation do you get after simplifying the left-hand side?

• 2 to the x minus 4/5 equals 2 to the 9/4

• 2 to the x plus 4/5 equals 2 to the 9/4

• 2 to the x plus 5/4 equals 2 to the 9/4

• 2 to the x equals 2 to the 9/4

What is the final value of x in the equation?

• 1.25

• 1.35

• 1.45

• 1.55