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Basic Notation

An exponential expression looks like this: $a^n$ .

5^4 = 5 \times 5 \times 5 \times 5 = 625

Read as: “5 raised to the power of 4”.

When you multiply two powers with the same base, you add the exponents.

a^m \times a^n = a^{m+n}

Why? $2^3 \times 2^2 = (2 \times 2 \times 2) \times (2 \times 2) = 2^{3+2} = 2^5$ .

When you take a power to another power, you multiply the exponents.

(a^m)^n = a^{m \times n}

Why? $(2^3)^2 = (2^3) \times (2^3) = 2^{3+3} = 2^{3 \times 2} = 2^6$ .

When multiplying different bases with the same exponent, you can multiply the bases first.

a^m \times b^m = (a \times b)^m

Example: $2^3 \times 5^3 = (2 \times 5)^3 = 10^3 = 1000$ .

When dividing powers with the same base, you subtract the exponents.

a^m \div a^n = a^{m-n}

Why?

\frac{2^5}{2^2} = \frac{2 \times 2 \times 2 \times 2 \times 2}{2 \times 2} = 2 \times 2 \times 2 = 2^3