To make algebraic expressions easier to work with, we can use some simple rules called the laws of indices. Here are the basic rules you need to remember:
Multiplication: When you multiply two numbers with the same base, you add the exponents.
This looks like:
(a^m \times a^n = a^{m+n})
Division: When you divide two numbers with the same base, you subtract the exponents.
This looks like:
(a^m \div a^n = a^{m-n})
Power of a Power: If you raise a power to another power, you multiply the exponents.
This looks like:
((a^m)^n = a^{m \times n})
Power of a Product: When you have a product (like (ab)) raised to a power, you can raise each part to that power.
This looks like:
((ab)^n = a^n \times b^n)
Power of a Quotient: If you have a fraction (like (\frac{a}{b})) raised to a power, you can raise the top and bottom to that power.
This looks like:
(\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n})
These rules help you simplify and solve math problems more easily. They are really important for understanding AS-Level math.
To make algebraic expressions easier to work with, we can use some simple rules called the laws of indices. Here are the basic rules you need to remember:
Multiplication: When you multiply two numbers with the same base, you add the exponents.
This looks like:
(a^m \times a^n = a^{m+n})
Division: When you divide two numbers with the same base, you subtract the exponents.
This looks like:
(a^m \div a^n = a^{m-n})
Power of a Power: If you raise a power to another power, you multiply the exponents.
This looks like:
((a^m)^n = a^{m \times n})
Power of a Product: When you have a product (like (ab)) raised to a power, you can raise each part to that power.
This looks like:
((ab)^n = a^n \times b^n)
Power of a Quotient: If you have a fraction (like (\frac{a}{b})) raised to a power, you can raise the top and bottom to that power.
This looks like:
(\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n})
These rules help you simplify and solve math problems more easily. They are really important for understanding AS-Level math.