What is ${(x^{- 3})}^{2} \cdot \frac{x^{5}}{x^{- 1}}$ $(x^-3) ^2 *x^5 / x^-1$ ?

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What is ${(x^{- 3})}^{2} \cdot \frac{x^{5}}{x^{- 1}}$ $(x^-3) ^2 *x^5 / x^-1$ ?

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Answer 1 · 2018-03-27T16:51:55

$1$ $1$

Explanation:

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

Answer 2 · 2018-03-27T16:54:50

$1$ $1$

Apply the laws of indices

Explanation:

${(x^{- 3})}^{2} \times \frac{x^{5}}{x^{- 1}} \leftarrow {(x^{m})}^{n} = x^{m n}$ $(x^-3)^2 xx x^5/x^-1" "larr (x^m)^n = x^(mn)$

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

$= \frac{1}{x^{6}} \times x^{5} \times x^{1} \leftarrow x^{m} \times x^{n} = x^{m + n}$ $= 1/x^6 xx x^5 xx x^1" "larr x^m xx x^n = x^(m+n)$

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

$= x^{0} \leftarrow \frac{x^{m}}{x^{n}} = x^{m - n}$ $=x^0" "larr x^m/x^n = x^(m-n)$

$= 1 \leftarrow x^{0} = 1$ $=1" "larr x^0=1$

Answer 3 · 2018-03-27T16:57:30

$= 1$ $color(magenta)(=1$

Explanation:

${(x^{- 3})}^{2} \cdot \frac{x^{5}}{x^{- 1}}$ $(x^(−3))^2⋅x^5/x^(−1$

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

$= x^{- 3 \times 2} \cdot \frac{x^{5}}{x^{- 1}}$ $=x^(-3xx2)⋅x^5/x^(−1$

$= x^{- 6} \cdot \frac{x^{5}}{x^{- 1}}$ $=x^(-6)⋅x^5/x^(−1$

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

$= x^{- 6} \cdot x^{5 - (- 1)}$ $=x^(-6)⋅x^(5-(-1))$

$= x^{- 6} \cdot x^{6}$ $=x^-6⋅x^6$

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

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

$= x^{0}$ $=x^0$

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

$x^{0} = 1$ $color(magenta)(x^0=1$

$- Hope this helps! :)$ $-"Hope this helps! :)"$

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