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 Depdendent Variable

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 Dependent Variable

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# Properties of Exponents

The table below summarizes the properties of exponents.

 Property Positive Integer Exponents Negative Integer Exponents Multiplication xm Â· xn = xm+n 32 Â· 34 = 32+4 = 36 Division Here, x ≠ 0. Power of a Power (xm)n = xmÂ·n (52)3 = 52Â·3 = 56 (5-2)-3 = 5(-2)Â·(-3) = 56 Power of a Product (x Â· y)n = xn Â· yn (5 Â· 7)3 = 53 Â· 73 Power of a Quotient Here, y ≠ 0.

The properties of exponents can be used to derive the following two formulas:

Formulas

Negative Exponents and Fractions

When a factor is moved to the other side of the fraction bar, we change the sign of the exponent.

Here, x ≠ 0 and y ≠ 0.

A fraction raised to a power is equal to the reciprocal of the fraction raised to the opposite power.

Here, x ≠ 0 and y ≠ 0.

We can use these formulas to rewrite expressions using positive exponents.