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. \newline5y5y4\frac{5y}{5y^4}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 8right chevron icon
Multiply and divide powers: variable basesright chevron icon

Full solution

Q. Simplify. Express your answer using positive exponents. \newline5y5y4\frac{5y}{5y^4}
  1. Divide and Simplify: Simplify the expression by dividing the numerator by the denominator.\newlineWe have the expression 5y5y4\frac{5y}{5y^4}. Since both the numerator and the denominator have the common factor 5y5y, we can simplify the expression by dividing both by 5y5y.\newline5y5y4=(55)×(yy4)\frac{5y}{5y^4} = \left(\frac{5}{5}\right) \times \left(\frac{y}{y^4}\right)
  2. Simplify Coefficients and Variables: Simplify the coefficients and the variables separately.\newlineThe coefficients 55\frac{5}{5} simplify to 11, and the variables y/y4y/y^4 simplify using the quotient rule for exponents, which states that am/an=a(m−n)a^m / a^n = a^{(m-n)} when m > n.\newline1×(y1/y4)=1×y(1−4)=1×y−31 \times (y^1/y^4) = 1 \times y^{(1-4)} = 1 \times y^{-3}
  3. Express Using Positive Exponents: Express the answer using positive exponents.\newlineSince the problem asks for positive exponents, we need to rewrite y−3y^{-3} as 1/y31/y^3.\newline1×y−3=1/y31 \times y^{-3} = 1/y^3
  4. Write Final Expression: Write the final simplified expression.\newlineThe final simplified expression is 1y3.\frac{1}{y^3}.

More problems from Multiply and divide powers: variable bases

Question
Write the expression using an exponent.\newline2×22 \times 2\newline______
Get tutor helpright-arrow

Posted 8 months ago

Question
Evaluate the expression. 4−42 4 - 4^2 ____
Get tutor helpright-arrow

Posted 8 months ago

Question
x2=4x^2 = 4
Get tutor helpright-arrow

Posted 7 months ago

Question
x2=9x^2 = 9
Get tutor helpright-arrow

Posted 9 months ago

Question
Solve for x. \newlinex2=0x^2 = 0 \newlineWrite your answer in simplified, rationalized form. \newlinex=x = _____ or x=x = _____
Get tutor helpright-arrow

Posted 9 months ago

Question
Solve for xx. \newline8=2x8 = 2^x \newline x=x = _____
Get tutor helpright-arrow

Posted 9 months ago

Question
Solve for xx. \newline6=7x6 = 7^x \newline x=x = _____
Get tutor helpright-arrow

Posted 9 months ago

Question
Select the equivalent expression.\newline((8−5)/(2−2))−4=?((8^{-5})/(2^{-2}))^{-4}=?\newlineChoose 11 answer:\newline(A) \newline(820)/(28)(8^{20})/(2^{8})\newline(B) \newline(26)/(89)(2^{6})/(8^{9})\newline(C) \newline(1)/(8⋅22)(1)/(8\cdot 2^{2})
Get tutor helpright-arrow

Posted 6 months ago

Question
Select the equivalent expression.\newline(b745)−3= ?\left(\frac{b^{7}}{4^{5}}\right)^{-3}=\,?\newlineChoose 11 answer:\newline(A) b21415\frac{b^{21}}{4^{15}}\newline(B) 415b21\frac{4^{15}}{b^{21}}\newline(C) b−21⋅4−15b^{-21}\cdot 4^{-15}
Get tutor helpright-arrow

Posted 7 months ago

Question
Select the equivalent expression.\newline(33⋅66)−3=(3^{3}\cdot6^{6})^{-3}=?\newlineChoose 11 answer:\newline(A) 139⋅618\frac{1}{3^{9}\cdot6^{18}}\newline(B) 61839\frac{6^{18}}{3^{9}}\newline(C) 39618\frac{3^{9}}{6^{18}}
Get tutor helpright-arrow

Posted 8 months ago

View all (114)

Related topics

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