Review Integer Exponents

We use an exponent to write down repeated multiplication: 2^5 reads “2 to the power of 5” and means 2\times 2\times 2\times 2\times 2=32.

Mutliply by yet another 2, and then we have 2^6=64.

Now divide by 2, and we return to 2^5=32.

Increasing the exponent by one means to multiply once more; decreasing an exponent by one means to divide once more. On this applet, move the slider to the right to multiply, move it to the left to divide, and notice the exponent as you do so:

Use this applet to become familiar (again?) with some common exponent values:

Laws of Exponents

Review the laws of integer exponents on these page:

Exponent Laws Development

Summary of Exponent Laws

    \begin{align*}{a^m \times a^n &= a^{m+n} \\[15pt] a^m \div a^n &= a^{m - n} \\[15pt] a^{-n}&=\frac{1}{a^n} \\[15pt] a^0&=1 \\[15pt] (a^m)^n&=a^{mn} \\[15pt] (a\cdot b)^n&=a^n \times b^n \\[15pt]  \Big(\frac{a}{b}\Big)^n&=\frac{a^n}{b^n}}\end{align*}

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Next: Factoring Expressions