4 answers
Question:

Find the sum of all the integer values of m that make the following equation true: $\left(2^m3^5\right)^m 9^7=\dfrac{\left(256\cdot3^m\right) ^m}{\left(\sqrt2\right)^{14}}$.

Answers

i can't see the picture : /

explanation:

step-by-step explanation:

answer: [tex]x=3\sqrt{2}[/tex]

step-by-step explanation:

you need to apply the pythagorean theorem:

[tex]a^2=b^2+c^2[/tex]

where "a" is the hypotenuse and "b" and "c" are the legs of the triangle.

you can observe in the figure that the value of the legs are:

[tex]b=3\\c=3[/tex]

then, substituting these values into [tex]a^2=b^2+c^2[/tex], you get that the value of the hypotenuse "x" is:

[tex]x^2=3^2+3^2[/tex]

[tex]x=\sqrt{18}[/tex]

to simplify   [tex]x=\sqrt{18}[/tex], you need to remember that:

[tex]\sqrt[n]{x^n}=x[/tex]

then, you must descompose 18 into its prime factors:

[tex]18=2*3*3=2*3^2[/tex]

substituting and simplifying, you get:

  [tex]x=\sqrt{2*3^2}[/tex]

[tex]x=3\sqrt{2}[/tex]

[tex]What is the value of x? leave your answer in simplest radical form.[/tex]

you can use a^2+ b^2=c^2

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