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Select the equivalent expression.

(x^(-3))/(x^(-6)*x^(-7))

x^(2)

x^(10)

(1)/(x^(10))

(1)/(x^(2))

Select the equivalent expression.\newlinex3x6x7 \frac{x^{-3}}{x^{-6} \cdot x^{-7}} \newlinex2 x^{2} \newlinex10 x^{10} \newline1x10 \frac{1}{x^{10}} \newline1x2 \frac{1}{x^{2}}

Full solution

Q. Select the equivalent expression.\newlinex3x6x7 \frac{x^{-3}}{x^{-6} \cdot x^{-7}} \newlinex2 x^{2} \newlinex10 x^{10} \newline1x10 \frac{1}{x^{10}} \newline1x2 \frac{1}{x^{2}}
  1. Simplify denominator: Simplify the denominator by adding the exponents of xx. When multiplying powers with the same base, you add the exponents. x6×x7=x6+7x^{-6} \times x^{-7} = x^{-6 + -7} = x13x^{-13}
  2. Add exponents: Divide the powers by subtracting the exponents.\newlineWhen dividing powers with the same base, you subtract the exponents.\newlinex3x13=x3(13)\frac{x^{-3}}{x^{-13}} = x^{-3 - (-13)}\newline=x3+13= x^{-3 + 13}\newline=x10= x^{10}

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