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 expression. Write your answers using integers or improper fractions. 2k-(1)/(2)((1)/(2)k+2) Answer:

Simplify the expression. Write your answers using integers or improper fractions.\newline2k−12(12k+2) 2 k-\frac{1}{2}\left(\frac{1}{2} k+2\right) \newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 7right chevron icon
Powers with decimal and fractional basesright chevron icon

Full solution

Q. Simplify the expression. Write your answers using integers or improper fractions.\newline2k−12(12k+2) 2 k-\frac{1}{2}\left(\frac{1}{2} k+2\right) \newlineAnswer:
  1. Distribute (1/2)(1/2): Distribute the (1/2)(1/2) across the terms inside the parentheses.\newline(1/2)((1/2)k+2)=(1/2)⋅(1/2)k+(1/2)⋅2(1/2)((1/2)k + 2) = (1/2)\cdot(1/2)k + (1/2)\cdot2
  2. Simplify multiplication: Simplify the multiplication inside the parentheses.\newline(12)∗(12)k=(14)k(\frac{1}{2})*(\frac{1}{2})k = (\frac{1}{4})k\newline(12)∗2=1(\frac{1}{2})*2 = 1\newlineSo, (12)((12)k+2)(\frac{1}{2})((\frac{1}{2})k + 2) becomes (14)k+1(\frac{1}{4})k + 1
  3. Rewrite with simplification: Rewrite the original expression with the simplified version of the parentheses. \newline2k−(12)(12k+2)2k - \left(\frac{1}{2}\right)\left(\frac{1}{2}k + 2\right) becomes 2k−(14k+1)2k - \left(\frac{1}{4}k + 1\right)
  4. Distribute negative sign: Distribute the negative sign across the terms in the parentheses. \newline2k−((1/4)k+1)=2k−(1/4)k−12k - ((1/4)k + 1) = 2k - (1/4)k - 1
  5. Combine like terms: Combine like terms.\newline2k−14k=84k−14k=74k2k - \frac{1}{4}k = \frac{8}{4}k - \frac{1}{4}k = \frac{7}{4}k\newlineSo, 2k−14k−12k - \frac{1}{4}k - 1 becomes 74k−1\frac{7}{4}k - 1
  6. Final simplified expression: The expression is now simplified. The final simplified expression is (74)k−1(\frac{7}{4})k - 1

More problems from Powers with decimal and fractional bases

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

Posted 1 year ago

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

Posted 1 year ago

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

Posted 1 year ago

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

Posted 1 year 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 1 year ago

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

Posted 1 year ago

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

Posted 1 year 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 11 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 1 year 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 1 year ago

View all (42)

Related topics

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