Exponents REVIEW

An exponent is a mathematical notation indicating the number of times a number (the base) is multiplied by itself. For example, in $$2^3$$ , 2 is the base and 3 is the exponent, meaning $$2 \times 2 \times 2$$ .

Simplifying an expression with exponents involves reducing it to its simplest form, often by applying the laws of exponents, such as the product of powers, quotient of powers, and power of a power.

The product of powers rule 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 quotient of powers rule states that when dividing two expressions with the same base, you subtract the exponents. For example, $$\frac{a^m}{a^n} = a^{m-n}$$ .

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

Expressing an exponent as a positive number involves rewriting negative exponents as fractions. For example, $$a^{-n} = \frac{1}{a^n}$$ .

To simplify, divide the coefficients (24/8 = 3) and subtract the exponents of k (12-2 = 10), resulting in $$3k^{10}$$ .

To simplify, divide the coefficients (30/10 = 3), subtract the exponents of x (3-2 = 1), and subtract the exponents of y (5-3 = 2), resulting in $$3xy^2$$ .

The simplified form is $$\frac{y^3}{x}$$ .

The simplified form is $$\frac{6}{y^2}$$ .