The index laws including negative and fractional powers, writing and calculating with standard form, and simplifying and rationalising surds.
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1.State the multiplication index law.
When multiplying powers of the same base, add the indices. a to the m times a to the n = a to the m plus n.
2.State the division index law.
When dividing powers of the same base, subtract the indices. a to the m divided by a to the n = a to the m minus n.
3.State the power of a power law.
Multiply the indices. (a to the m) to the n = a to the mn.
4.What does any number to the power zero equal?
1
5.What does a negative index mean?
The reciprocal. a to the minus n = 1 divided by a to the n.
6.Work out 2 to the power minus 3.
1 divided by 8.
7.What does a power of one half mean?
The square root.
8.What does a power of one third mean?
The cube root.
9.What does a power of two thirds mean?
Cube root first, then square the result.
10.Work out 8 to the power two thirds.
Cube root of 8 is 2, and 2 squared is 4.
11.Simplify x to the 5 times x to the 3.
x to the 8.
12.Simplify x to the 7 divided by x to the 2.
x to the 5.
13.What is standard form?
A number written as a x 10 to the n, where a is at least 1 and less than 10, and n is an integer.
14.Write 4500 in standard form.
4.5 x 10 to the 3.
15.Write 0.0032 in standard form.
3.2 x 10 to the minus 3.
16.How do you multiply numbers in standard form?
Multiply the number parts, add the powers, then adjust so the number part is between 1 and 10.
17.Work out (2 x 10 to the 3) multiplied by (4 x 10 to the 5).
8 x 10 to the 8.
18.How do you divide numbers in standard form?
Divide the number parts and subtract the powers.
19.Why must the number part be between 1 and 10?
That is the definition of standard form, and it makes numbers directly comparable by their power of ten.
20.What is a surd?
A root that cannot be simplified to a whole number, so it is left in root form as an exact value.
21.How do you simplify a surd?
Look for a square factor. The square root of 50 = the square root of 25 times 2 = 5 times the square root of 2.
22.Simplify the square root of 72.
The square root of 36 times 2 = 6 times the square root of 2.
23.What is the square root of a multiplied by the square root of a?
a
24.What does rationalising the denominator mean?
Removing a surd from the bottom of a fraction, by multiplying top and bottom by that surd.
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