Exponent Rules

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.

The base is the number that is being multiplied. In $$2^7=128$$ , the base is 2.

When multiplying two exponents with the same base, you keep the base the same and add the exponents. For example, $$x^2 \times x^3 = x^{2+3} = x^5$$ .

When raising an exponent to another exponent, you multiply the exponents. For example, $$(x^2)^3 = x^{2 \times 3} = x^6$$ .

When raising a product to an exponent, you apply the exponent to each factor. For example, $$(xy)^2 = x^2y^2$$ .

Any non-zero number raised to the power of zero equals one. For example, $$5^0 = 1$$ .

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent. For example, $$x^{-2} = \frac{1}{x^2}$$ .

$$x^{3+4} = x^7$$ .

$$y^{5+2} = y^7$$ .

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