Exercises: Power Laws

Term 1:

$x^{10}$

Term 2:

$x^{-6}$

Term 3:

${\left(x^{-2}\right)}^4=x^{-2\cdot 4}=x^{-8}$

Apply the power laws.

Term 4:

$x^5+x^5=2x^5$

Term 5:

${(-x)}^6=x^6$

The minus can be omitted here, because the power is even and $(-1{)}^2=1$.

Term 6:

$x^{-8}$

Term 7:

$x^{15}:x^5=x^{15-5}=x^{10}$

Apply the power laws.

Term 8:

$x^{-22}\cdot x^{16}=x^{-22+16}=x^{-6}$

Apply the power laws.

Term 9:

$-x^6=-(x{)}^6=-x^6$

Equivalent terms:

• Term 1 and term 7 are both equal to $x^{10}$.

• Term 2 and term 8 are both equal to $x^6$.

• Term 3 and term 6 are both equal to $x^{-8}$.