Maths-
General
Easy

Question

If fraction numerator square root of straight x to the power of 5 end root over denominator cube root of straight x to the power of 4 end root end fraction space equals space straight a to the power of straight a over straight b end exponent for all positive values of x, what is the value of straight a over straight b ?

The correct answer is: 1.167


    fraction numerator square root of straight x to the power of 5 end root over denominator cube root of straight x to the power of 4 end root end fraction space equals space straight x to the power of straight a over straight b end exponent text   as   end text open square brackets straight a-th root of straight x to the power of straight b end root text end text equals space straight x to the power of straight a over straight b end exponent close square brackets
    So, straight x to the power of begin display style 5 over 2 end style end exponent over straight x to the power of begin display style 4 over 3 end style end exponent space equals space straight x to the power of straight a over straight b end exponent open square brackets straight x to the power of straight a over straight x to the power of straight b space equals space straight x to the power of left parenthesis straight a space minus space straight b right parenthesis end exponent close square brackets
    x to the power of open parentheses 5 over 2 space minus space 4 over 3 close parentheses end exponent space equals space x to the power of a over b end exponent
    not stretchy rightwards double arrow space straight a over straight b space equals space 5 over 2 space minus space 4 over 3 space not stretchy rightwards double arrow space fraction numerator begin display style straight a end style over denominator straight b end fraction = 7 over 6 or 1.66
    straight a over straight b space equals space 7 over 6 or 1.167

    Related Questions to study

    General
    Maths-

    (x2 - 3) – (- 3x2 + 5) Which of the following expressions is equivalent to the one above?

    (x2 - 3) – (- 3x2 + 5) Which of the following expressions is equivalent to the one above?

    Maths-General
    General
    Maths-


    The points plotted in the coordinate plane above represent the possible numbers of wallflowers and cornflowers that someone can buy at the Garden the Store in order to spend exactly $24.00 total on the two types of flowers. The price of each wallflower is the same and the price of each cornflower is the same. What is the price, in dollars, of 1 cornflower? (Disregard the $ sign when gridding your answer. For example, if your answer is $9.87, grid 9.87 )


    The points plotted in the coordinate plane above represent the possible numbers of wallflowers and cornflowers that someone can buy at the Garden the Store in order to spend exactly $24.00 total on the two types of flowers. The price of each wallflower is the same and the price of each cornflower is the same. What is the price, in dollars, of 1 cornflower? (Disregard the $ sign when gridding your answer. For example, if your answer is $9.87, grid 9.87 )

    Maths-General
    General
    Maths-

    x + x = 9
    What value of x satisfies the equation given?

    x + x = 9
    What value of x satisfies the equation given?

    Maths-General
    parallel
    General
    Maths-

    Feeding Information for Boarded Pets

    The table above shows the kinds of foods that are fed to the cats and dogs currently boarded at a pet care facility. What fraction of the dogs are fed only dry food?

    Feeding Information for Boarded Pets

    The table above shows the kinds of foods that are fed to the cats and dogs currently boarded at a pet care facility. What fraction of the dogs are fed only dry food?

    Maths-General
    General
    Maths-

    ax + by = b
    In the equation above, a & b are constants and 0 < a < b. Which of the following could represent the graph of the equation in the xy-plane?

    ax + by = b
    In the equation above, a & b are constants and 0 < a < b. Which of the following could represent the graph of the equation in the xy-plane?

    Maths-General
    General
    Maths-

    (7532 + 100 y2) + 10 (10 y2 – 110) The expression above can be written in the form
    ay2 + b , where a and b are constants. What is the value of a + b ?

    (7532 + 100 y2) + 10 (10 y2 – 110) The expression above can be written in the form
    ay2 + b , where a and b are constants. What is the value of a + b ?

    Maths-General
    parallel
    General
    Maths-

    h(t) = -16t2 + 48t +72
    If air resistance is ignored, the function h defined above models the height above ground, in feet, of a toy rocket t seconds after it is launched from the roof of building. Based on the model, what is the height above ground, in feet, of the toy rocket 1 second after launch?

    h(t) = -16t2 + 48t +72
    If air resistance is ignored, the function h defined above models the height above ground, in feet, of a toy rocket t seconds after it is launched from the roof of building. Based on the model, what is the height above ground, in feet, of the toy rocket 1 second after launch?

    Maths-General
    General
    Maths-

    x squared minus 12 x plus 35 equals 0
    What is the sum of the solutions to the given equation?

    x squared minus 12 x plus 35 equals 0
    What is the sum of the solutions to the given equation?

    Maths-General
    General
    Maths-

    A pizza parlor sells pizza slices for $ 3 each and calzones for $ 4 each. A group of friends spent $ 51 on pizza slices and calzones at the parlor. If they bought 6 calzones, how many pizza slices did they buy?

    A pizza parlor sells pizza slices for $ 3 each and calzones for $ 4 each. A group of friends spent $ 51 on pizza slices and calzones at the parlor. If they bought 6 calzones, how many pizza slices did they buy?

    Maths-General
    parallel
    General
    Maths-

    The graph of a line in the x y-plane passes through the point (1, 4) and crosses the x-axis at the point (2, 0) . The line crosses the y-axis at the point (0, b) . What is the value of b ?

    The graph of a line in the x y-plane passes through the point (1, 4) and crosses the x-axis at the point (2, 0) . The line crosses the y-axis at the point (0, b) . What is the value of b ?

    Maths-General
    General
    Maths-

    3x + y = 29
    x = 2
    If (x , y) is the solution to the given system of equations, what is the value of y ?

    3x + y = 29
    x = 2
    If (x , y) is the solution to the given system of equations, what is the value of y ?

    Maths-General
    General
    Maths-

    The dimensions of a right rectangular prism are 4 inches by 5 inches by 6 inches. What is the surface area, in square inches, of the prism?

    The dimensions of a right rectangular prism are 4 inches by 5 inches by 6 inches. What is the surface area, in square inches, of the prism?

    Maths-General
    parallel
    General
    Maths-

    The number of radians in a 720-degree angle can be written as a pi, where a is a constant. What is the value of a ?

    The number of radians in a 720-degree angle can be written as a pi, where a is a constant. What is the value of a ?

    Maths-General
    General
    Maths-

    i2 + (-i)2
    In the complex number system, what is the value of the given expression? (Note: i = square root of negative 1 end root )

    i2 + (-i)2
    In the complex number system, what is the value of the given expression? (Note: i = square root of negative 1 end root )

    Maths-General
    General
    Maths-


    In the figure above, MQ and NR intersect at point P, NP = QP  , and MP = PR  . What is the measure, in degrees, of ∠QMR ? (Disregard the degree symbol when gridding your answer.)


    In the figure above, MQ and NR intersect at point P, NP = QP  , and MP = PR  . What is the measure, in degrees, of ∠QMR ? (Disregard the degree symbol when gridding your answer.)

    Maths-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.