Simplifying Exponential Expressions

When multiplying two expressions with the same base, you add the exponents: $$a^m \times a^n = a^{m+n}$$ .

When raising a power to another power, you multiply the exponents: $$(a^m)^n = a^{m \times n}$$ .

When dividing two expressions with the same base, you subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$ .

$$x^4$$ .

$$x^{10}$$ .

Any non-zero base raised to the power of zero equals one: $$a^0 = 1$$ .

A negative exponent indicates the reciprocal: $$a^{-n} = \frac{1}{a^n}$$ .

$$x$$ .

$$x^{5-2}y^{3-2} = x^3y$$ .

When multiplying two expressions with the same base, you add the exponents: $$a^m \times a^n = a^{m+n}$$ .