# What is (x^-3) ^2 *x^5 / x^-1?

Mar 27, 2018

$1$

#### Explanation:

${\left({x}^{-} 3\right)}^{2} \cdot {x}^{5} / {x}^{-} 1 = {x}^{- 3 \cdot 2} \cdot {x}^{5} \cdot {x}^{1} = {x}^{-} 6 \cdot {x}^{6} = {x}^{6} / {x}^{6} = 1$

Mar 27, 2018

$1$

Apply the laws of indices

#### Explanation:

${\left({x}^{-} 3\right)}^{2} \times {x}^{5} / {x}^{-} 1 \text{ } \leftarrow {\left({x}^{m}\right)}^{n} = {x}^{m n}$

$= {x}^{-} 6 \times {x}^{5} / {x}^{-} 1 \text{ } \leftarrow {x}^{-} m = \frac{1}{x} ^ m$

$= \frac{1}{x} ^ 6 \times {x}^{5} \times {x}^{1} \text{ } \leftarrow {x}^{m} \times {x}^{n} = {x}^{m + n}$

$= {x}^{6} / {x}^{6}$

$= {x}^{0} \text{ } \leftarrow {x}^{m} / {x}^{n} = {x}^{m - n}$

$= 1 \text{ } \leftarrow {x}^{0} = 1$

Mar 27, 2018

color(magenta)(=1

#### Explanation:

(x^(−3))^2⋅x^5/x^(−1

$\text{Applying the law:}$ color(blue)((a^m)^n=a^(mn;

=x^(-3xx2)⋅x^5/x^(−1

=x^(-6)⋅x^5/x^(−1

$\text{Applying the law:}$ color(blue)(a^m/a^n=a^(m-n)

=x^(-6)⋅x^(5-(-1))

=x^-6⋅x^6

$\text{Applying the law:}$ color(blue)(a^m⋅a^n=a^(m+n);"

$= {x}^{- 6 + 6}$

$= {x}^{0}$

$\text{Applying the law:}$ color(blue)( a^0=1

color(magenta)(x^0=1

$- \text{Hope this helps! :)}$