Advanced Indices
Maths: Edexcel IGCSE Higher, topic 1.4.4
Advanced Powers and Roots
Powers and roots can be expressed (written) in more than one way.
Negative powers
- Negative powers are equivalent (the same as) to 1 ÷ the number.
Half powers
- Half powers are the same as a square root.
Third powers
- Third powers are the same as cube roots.
Fraction powers
- Deal with one part of the fraction at a time.
Calculating Fractional Powers
Fractions can be powers.
Step 1 with a positive fractional power
- The denominator of the fractional power becomes the root of the number.
- The numerator of the fractional power becomes the power of the number.
Step 2 with a positive fractional power
- Calculate the root of the number first.
Step 3 with a positive fractional power
- Calculate the power of the answer to the previous step.
Step 1 with a negative fractional power
- Go through the same process as with a positive fractional power.
- But, it is now equivalent (the same as) to 1 ÷ the number.
Step 2 with a negative fractional power
- Calculate the answer to the positive fractional power.
- Insert the answer as the denominator to a fraction. The numerator is 1.
- The answer can either remain as a fraction or you can convert it into a decimal.
Test yourself on Advanced Indices
What is an equivalent way of writing the power shown in the image?
What is an equivalent way of writing the power shown in the image?
What is an equivalent way of writing the power shown in the image?
What is an equivalent way of writing the power shown in the image?
What is an equivalent way of writing the power shown in the image?