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:

Perform the operation and simplify the answer fully. (10)/(9x^(3))÷(5)/(7x^(2)) Answer:

Perform the operation and simplify the answer fully.\newline109x3÷57x2 \frac{10}{9 x^{3}} \div \frac{5}{7 x^{2}} \newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Operations with rational exponentsright chevron icon

Full solution

Q. Perform the operation and simplify the answer fully.\newline109x3÷57x2 \frac{10}{9 x^{3}} \div \frac{5}{7 x^{2}} \newlineAnswer:
  1. Rewrite Division: Rewrite the division of fractions as multiplication by the reciprocal.\newlineTo divide by a fraction, you multiply by its reciprocal. The reciprocal of (5)/(7x2)(5)/(7x^{2}) is (7x2)/(5)(7x^{2})/(5).
  2. Set Up Multiplication: Set up the multiplication of the two fractions. 109x3×7x25\frac{10}{9x^{3}} \times \frac{7x^{2}}{5}
  3. Multiply Numerators and Denominators: Multiply the numerators and the denominators separately.\newline(10×7x2)/(9x3×5)(10 \times 7x^{2}) / (9x^{3} \times 5)
  4. Perform Multiplication: Perform the multiplication in the numerator and the denominator.\newline70x245x3\frac{70x^{2}}{45x^{3}}
  5. Simplify Fraction: Simplify the fraction by canceling common factors.\newlineBoth the numerator and the denominator have common factors of 55 and x2x^{2}.\newline(70/5)x2(45/5)x3\frac{(70/5)x^{2}}{(45/5)x^{3}}
  6. Simplify Numbers and Terms: Simplify the numbers and the xx terms separately.14x29x3\frac{14x^{2}}{9x^{3}}
  7. Apply Exponent Laws: Apply the laws of exponents to simplify the xx terms.\newlineWhen dividing like bases, subtract the exponents: x2x3=x2−3=x−1\frac{x^{2}}{x^{3}} = x^{2-3} = x^{-1}.\newline149x1\frac{14}{9x^{1}}
  8. Rewrite with Positive Exponent: Rewrite the expression with a positive exponent.\newlineSince x−1x^{-1} is the same as 1x\frac{1}{x}, the final simplified form is:\newline149x\frac{14}{9x}

More problems from Operations with rational exponents

Question
f(x)=6x+52−14+5x f(x)=\frac{6 x+5}{2-\sqrt{14+5 x}} \newlineWe want to find lim⁡x→−2f(x) \lim _{x \rightarrow-2} f(x) .\newlineWhat happens when we use direct substitution?\newlineChoose 11 answer:\newline(A) The limit exists, and we found it!\newline(B) The limit doesn't exist (probably an asymptote).\newline(C) The result is indeterminate.
Get tutor helpright-arrow

Posted 9 months ago

Question
Let x4+y2=17 x^{4}+y^{2}=17 .\newlineWhat is the value of d2ydx2 \frac{d^{2} y}{d x^{2}} at the point (−2,1) (-2,1) ?\newlineGive an exact number.
Get tutor helpright-arrow

Posted 8 months ago

Question
What is the area of the region bound by the graphs of f(x)=x−2,g(x)=14−x f(x)=\sqrt{x-2}, g(x)=14-x , and x=2 x=2 ?\newlineChoose 11 answer:\newline(A) 196 \frac{19}{6} \newline(B) 992 \frac{99}{2} \newline(C) 1512 \frac{151}{2} \newline(D) 452 \frac{45}{2}
Get tutor helpright-arrow

Posted 7 months ago

Question
Let g(x)=x43 g(x)=x^{\frac{4}{3}} .\newlineg′(27)= g^{\prime}(27)=
Get tutor helpright-arrow

Posted 8 months ago

Question
Simplify ln⁡(1e) \ln \left(\frac{1}{\sqrt{e}}\right) \newlineAnswer:
Get tutor helpright-arrow

Posted 9 months ago

Question
Simplify ln⁡(1e) \ln \left(\frac{1}{e}\right) \newlineAnswer:
Get tutor helpright-arrow

Posted 9 months ago

Question
y=(sin⁡−1(5x2))3y=(\sin^{-1}(5x^{2}))^{3}
Get tutor helpright-arrow

Posted 8 months ago

Question
(10x3−5x2−6x)÷(2x2)\left(10x^{3}-5x^{2}-6x\right)\div\left(2x^{2}\right)
Get tutor helpright-arrow

Posted 8 months ago

Question
y=cos⁡4xsin⁡4xy=\cos^{4}x\sin^{4}x
Get tutor helpright-arrow

Posted 8 months ago

Question
35−310\frac{3}{5}-\frac{3}{10}
Get tutor helpright-arrow

Posted 8 months ago

View all (333)

Related topics

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