To evaluate the expression, we use the division rule for indices, which states that .Applying this rule to the given expression:Finally, we calculate the value of :Thus, the value of the expression is 81.

Write as a product of its prime factors.Give your answer in index form.

Goal: We need to write as a product of its prime factors in index form.Step 1: First, express the number 14 as a product of its prime factors.Step 2: Substitute the prime factors of 14 and the given expression for into . This sets up the calculation by showing the product of all prime factors involved.This step shows a correct method to combine the expressions. M1Step 3: Group the factors with the same prime base and apply the law of indices to simplify the expression.This is the correct final answer in index form. A1Conclusion: Therefore, as a product of its prime factors is .

Goal: Calculate the value of .Step 1: Apply the law of indices for multiplication, which states that for the same base , .Step 2: Evaluate the resulting power. Any non-zero number raised to the power of 0 is equal to 1.Conclusion: The value of is 1.

Goal: Write in the form .Step 1: Express the numbers 27 and 81 as powers of base 3.We can write and .Step 2: Substitute these into the expression and simplify using the laws of indices.The calculation is as follows:M2Conclusion: Therefore, in the form is .

Question Hub

IGCSE (CAMBRIDGE)|9th and 10th|Extended Maths (0580)

Flash Card Study Notes Previous Year Question Hub Practice Set Question Hub

Question year

Question type

Difficulty level

Select time zone

17 Qs

QUESTION:1

EasyPaper 2Subjective2025

Loading whiteboard...

QUESTION:2

EasyPaper 2Subjective2025

Loading whiteboard...

QUESTION:3

EasyPaper 2Subjective2025

Loading whiteboard...

QUESTION:4

MediumPaper 2Subjective2025

Loading whiteboard...