Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify the following expression to simplest form using only positive exponents. (32x^(-40)y^(-20))^(-(1)/(5)) Answer:

Simplify the following expression to simplest form using only positive exponents.\newline(32x−40y−20)−15 \left(32 x^{-40} y^{-20}\right)^{-\frac{1}{5}} \newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Multiplication with rational exponentsright chevron icon

Full solution

Q. Simplify the following expression to simplest form using only positive exponents.\newline(32x−40y−20)−15 \left(32 x^{-40} y^{-20}\right)^{-\frac{1}{5}} \newlineAnswer:
  1. Apply Negative Exponent Rule: Apply the negative exponent rule which states that a−n=1ana^{-n} = \frac{1}{a^n}.
    (32x−40y−20)−15(32x^{-40}y^{-20})^{-\frac{1}{5}}
    =1(32x−40y−20)15= \frac{1}{(32x^{-40}y^{-20})^{\frac{1}{5}}}
  2. Apply Power of a Power Rule: Apply the power of a power rule which states that (am)n=am∗n(a^m)^n = a^{m*n}.\newline1(32x−40y−20)15\frac{1}{(32x^{-40}y^{-20})^{\frac{1}{5}}}\newline= 13215×x−40×(15)×y−20×(15)\frac{1}{32^{\frac{1}{5}} \times x^{-40\times(\frac{1}{5})} \times y^{-20\times(\frac{1}{5})}}
  3. Simplify Exponents: Simplify the exponents by multiplying them with 15\frac{1}{5}.1(3215⋅x−8⋅y−4)\frac{1}{(32^{\frac{1}{5}} \cdot x^{-8} \cdot y^{-4})}
  4. Simplify Fifth Root: Simplify the fifth root of 3232. 321/532^{1/5} is the same as the fifth root of 3232, which is 22 because 25=322^5 = 32. 12⋅x−8⋅y−4\frac{1}{2 \cdot x^{-8} \cdot y^{-4}}
  5. Apply Negative Exponent Rule: Apply the negative exponent rule again to move the xx and yy terms to the numerator.\newline12⋅x−8⋅y−4\frac{1}{2 \cdot x^{-8} \cdot y^{-4}}\newline= x8⋅y42\frac{x^8 \cdot y^4}{2}

More problems from Multiplication with rational exponents

Question
Simplify.\newline811281^{\frac{1}{2}}\newline_____________
Get tutor helpright-arrow

Posted 9 months ago

Question
Simplify.\newline(−32)1/5(-32)^{1/5}\newline______
Get tutor helpright-arrow

Posted 9 months ago

Question
Simplify. Assume all variables are positive.\newlinew43w73\frac{w^{\frac{4}{3}}}{w^{\frac{7}{3}}}\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Simplify. Assume all variables are positive.\newline(2r13)8(2r^{\frac{1}{3}})^8\newline\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Simplify. Assume all variables are positive.\newlinev74⋅v94v^{\frac{7}{4}} \cdot v^{\frac{9}{4}}\newline\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______\newline
Get tutor helpright-arrow

Posted 5 months ago

Question
Simplify.\newline114⋅1141^{\frac{1}{4}} \cdot 1^{\frac{1}{4}}\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Simplify. \newline32(−1/5)32^{(-1/5)}
Get tutor helpright-arrow

Posted 7 months ago

Question
Simplify. Assume all variables are positive.\newlinew32w52\frac{w^{\frac{3}{2}}}{w^{\frac{5}{2}}}\newline\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______\newline
Get tutor helpright-arrow

Posted 9 months ago

Question
Simplify. Assume all variables are positive.\newline(27x)23(27x)^{\frac{2}{3}}\newline\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______
Get tutor helpright-arrow

Posted 8 months ago

Question
Simplify. Assume all variables are positive.\newlinex14x114\frac{x^{\frac{1}{4}}}{x^{\frac{11}{4}}}\newline\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______\newline
Get tutor helpright-arrow

Posted 7 months ago

View all (744)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant