A-Level Revision - Pure Maths 09
B1 Laws of Indices and Surds - Theory
The laws of indices are methods and rules surrounding the manipulation around Surds are numbers left in ‘square root form’ or ‘cube root form’ etc
powers across integers and algebraic expressions.
Similiar to indices, surds can be more easily manipulated when the number or algebra
being rooted is the same. Certain rules will not work if what is being rooted is not the
same.
In order to manipulate indices, it is required that the two or more expressions being
manipulated have the same base.
For example,
This only works because ‘b’ is rooted within both of what is being added.
For example if you wanted to multiply by , you would be unable to apply the
laws of indices as the expressions have different bases (a and b). 1.
2.
Laws of Indices:
Rules of Surds
1. - If you multiply expressions add the powers.
3.
2. - If you divide expressions subtract the powers.
4.
3. - If a power is to the power of something, multiply powers.
Rationalising the Denominator is where we convert the denominator of a fractional
4. - Put both bases to the same power from an irrational number to a rational number.
Multiply by surd
5. - It is just the base Example 1.
6. - Anything to the power of 0 is 1
7. - The denominator of the fractional power, is the root of the base. Example 2.
8. - Rule applies for above, numerator remains to power of base.
9. - A negative power produces the reciprocal of the base.
Multiply by the conjugate in cases where it is a surd and a number.
B1 Laws of Indices and Surds - Theory
The laws of indices are methods and rules surrounding the manipulation around Surds are numbers left in ‘square root form’ or ‘cube root form’ etc
powers across integers and algebraic expressions.
Similiar to indices, surds can be more easily manipulated when the number or algebra
being rooted is the same. Certain rules will not work if what is being rooted is not the
same.
In order to manipulate indices, it is required that the two or more expressions being
manipulated have the same base.
For example,
This only works because ‘b’ is rooted within both of what is being added.
For example if you wanted to multiply by , you would be unable to apply the
laws of indices as the expressions have different bases (a and b). 1.
2.
Laws of Indices:
Rules of Surds
1. - If you multiply expressions add the powers.
3.
2. - If you divide expressions subtract the powers.
4.
3. - If a power is to the power of something, multiply powers.
Rationalising the Denominator is where we convert the denominator of a fractional
4. - Put both bases to the same power from an irrational number to a rational number.
Multiply by surd
5. - It is just the base Example 1.
6. - Anything to the power of 0 is 1
7. - The denominator of the fractional power, is the root of the base. Example 2.
8. - Rule applies for above, numerator remains to power of base.
9. - A negative power produces the reciprocal of the base.
Multiply by the conjugate in cases where it is a surd and a number.
