1 Answer

Paul Tucker · Answer 1 · 2023-02-11T15:47:45+0000

There are several laws of exponents. Let's see each of them.

Product of powers with equal bases.

When we have the product of two powers with equal bases, we just have to sum their exponents.

$x^3\cdot x^2=x^(3+2)=x^5$

When we have the division of two powers with equal bases, we just have to subtract their exponents.

When we have power inside another power, we just have to multiply the exponents.

$(x^2)^3=x^(2\cdot3)=x^6$

The power of a product between two factors is equal to the product of their powers.

$(x\cdot y)^5=x^5\cdot y^5$

This means we can separate the powers.

The powers of a division between two factors are equal to the division of their powers.

$(\frac{x^{}}{y})^2=(x^2)/(y^2)$

All roots have an equivalent fractional exponent, as follows

$\sqrt[4]{x^2}=x^{(2)/(4)}$

Observe that the exponent of the power is the numerator and the exponent of the root is the denominator.