Properties of Exponents

An exponent is a number that indicates how many times to multiply the base by itself. For example, in $$2^3$$ , 2 is the base and 3 is the exponent, meaning $$2 \times 2 \times 2$$ .

The product of powers property states that when multiplying two expressions with the same base, you add the exponents. For example, $$a^m \times a^n = a^{m+n}$$ .

The power of a power property states that when raising an exponent to another exponent, you multiply the exponents. For example, $$(a^m)^n = a^{m \times n}$$ .

The power of a product property states that when raising a product to an exponent, you can distribute the exponent to each factor. For example, $$(ab)^n = a^n \times b^n$$ .

The zero exponent rule states that any non-zero base raised to the power of zero equals one. For example, $$a^0 = 1$$ , where @@a eq 0@@.

The negative exponent rule states that a negative exponent indicates the reciprocal of the base raised to the opposite positive exponent. For example, $$a^{-n} = \frac{1}{a^n}$$ .

$$c^7$$ .

$$1$$ .

multiply.

$$8x^6$$ .