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. Express your answer using positive exponents.\newliner−2r−7⋅r8\frac{r^{-2}}{r^{-7} \cdot r^{8}}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Simplify exponential expressions using exponent rulesright chevron icon

Full solution

Q. Simplify. Express your answer using positive exponents.\newliner−2r−7⋅r8\frac{r^{-2}}{r^{-7} \cdot r^{8}}
  1. Identify Operation for Exponents: Identify the operation needed for the exponents −2-2, −7-7, and 88. When dividing powers with the same base, we subtract the exponents. When multiplying, we add the exponents.
  2. Simplify Denominator: Simplify the denominator r−7×r8r^{-7} \times r^{8}. We add the exponents because the powers of rr are being multiplied. r−7×r8=r(−7+8)=r1r^{-7} \times r^{8} = r^{(-7 + 8)} = r^{1}
  3. Rewrite Using Simplified Denominator: Rewrite the original expression using the simplified denominator. r−2/(r−7⋅r8)r^{-2}/(r^{-7} \cdot r^{8}) becomes r−2/r1.r^{-2}/r^{1}.
  4. Simplify Expression: Simplify the expression r−2/r1r^{-2}/r^{1}. We subtract the exponent in the denominator from the exponent in the numerator because the powers of rr are being divided. r−2/r1=r(−2−1)=r−3r^{-2}/r^{1} = r^{(-2 - 1)} = r^{-3}
  5. Express Answer Using Positive Exponents: Express the answer using positive exponents.\newlineSince r−3r^{-3} means 11 divided by r3r^3, we can rewrite the expression as:\newliner−3=1r3r^{-3} = \frac{1}{r^3}

More problems from Simplify exponential expressions using exponent rules

Question
Evaluate.\newline22=2^2 = _____
Get tutor helpright-arrow

Posted 10 months ago

Question
Evaluate. Write your answer as a fraction or whole number.\newline(14)4(\frac{1}{4})^4 = _____
Get tutor helpright-arrow

Posted 6 months ago

Question
Which is equal to 9−619^{-61}?
Get tutor helpright-arrow

Posted 6 months ago

Question
Simplify. \newlineExpress your answer using positive exponents.\newline r5⋅r8r^5 \cdot r^8
Get tutor helpright-arrow

Posted 6 months ago

Question
Simplify. Express your answer using a single exponent.\newline(h2)6(h^2)^6\newline______
Get tutor helpright-arrow

Posted 6 months ago

Question
Simplify. Express your answer using positive exponents.\newline(9p5)(5p8)(9p^5)(5p^8)\newline_____________
Get tutor helpright-arrow

Posted 6 months ago

Question
Simplify. Express your answer using positive exponents.\newline(2v3)(4v)(5v)(2v^3)(4v)(5v)\newline______
Get tutor helpright-arrow

Posted 10 months ago

Question
Simplify. Express your answer using a single exponent.\newline(5z8)2(5z^8)^2\newline_____________
Get tutor helpright-arrow

Posted 6 months ago

Question
Simplify. Express your answer using positive exponents.\newliner9⋅r8⋅r-5 r^9 \cdot r^8 \cdot r^{\text{-}5} \newline______
Get tutor helpright-arrow

Posted 6 months ago

Question
Which expression is equivalent to 6×686 \times 6^8?\newlineChoices:\newline169\frac{1}{6^9}\newline686^8\newline168\frac{1}{6^8}\newline696^9
Get tutor helpright-arrow

Posted 9 months ago

View all (196)

Related topics

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