Exponent Product and Power Rules

To multiply two powers with the same base, add the exponents. For example, $$x^a \times x^b = x^{a+b}$$ .

To raise a power to another power, multiply the exponents. For example, $$(x^a)^b = x^{a \times b}$$ .

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

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

$$(2x^3)(3x^2) = 6x^{3+2} = 6x^5$$ .

The area is calculated by multiplying the sides: $$5x^2 \times 2x^3 = 10x^{2+3} = 10x^5$$ .

Using the product rule, $$a^3 \times a^4 = a^{3+4} = a^7$$ .

Using the power of a power rule, $$(x^2)^3 = x^{2 \times 3} = x^6$$ .

Using the negative exponent rule, $$x^{-2} = \frac{1}{x^2}$$ .

According to the zero exponent rule, $$7^0 = 1$$ .