There are several laws of exponents. Let's see each of them.
When we have the product of two powers with equal bases, we just have to sum their exponents.
[tex]x^3\cdot x^2=x^{3+2}=x^5[/tex]When we have the division of two powers with equal bases, we just have to subtract their exponents.
[tex]\frac{x^3}{x^2}=x^{3-2}=x^1[/tex]When we have power inside another power, we just have to multiply the exponents.
[tex](x^2)^3=x^{2\cdot3}=x^6[/tex]The power of a product between two factors is equal to the product of their powers.
[tex](x\cdot y)^5=x^5\cdot y^5[/tex]This means we can separate the powers.
The powers of a division between two factors are equal to the division of their powers.
[tex](\frac{x^{}}{y})^2=\frac{x^2}{y^2}[/tex]All roots have an equivalent fractional exponent, as follows
[tex]\sqrt[4]{x^2}=x^{\frac{2}{4}}[/tex]Observe that the exponent of the power is the numerator and the exponent of the root is the denominator.
