Write each of the following functions in the form: f(x)=kx^p?

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Write each of the following functions in the form: f(x)=kx^p?

After I simplified the expression, how would I write the answers in f(x)=kx^p form?

1 Answer

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Answer 1 · 2017-11-14T12:13:40

$see explanation$ $"see explanation"$

Explanation:

$using the laws of exponents$ $"using the "color(blue)"laws of exponents"$

$∙ x a^{m} \times a^{n} \Leftrightarrow a^{(m + n)}$ $•color(white)(x)a^mxxa^nhArra^((m+n))$

#•color(white)(x)a^m/a^n=a^((m-n))

$∙ x a^{\frac{1}{2}} \Leftrightarrow \sqrt{a}$ $•color(white)(x)a^(1/2)hArrsqrta$

$∙ x a^{\frac{m}{n}} \Leftrightarrow \sqrt[n]{a^{m}}$ $•color(white)(x)a^(m/n)hArrroot(n)(a^m)$

$the form f (x) = k x^{p} \leftarrow k is a constant$ $"the form "f(x)=kx^plarrcolor(blue)"k is a constant"$

$(a)$ $(a)$

$R (t) = \frac{4}{\sqrt{16 t}} = \frac{4}{\sqrt{16} \times \sqrt{t}} = \frac{4}{4 t^{\frac{1}{2}}} = 1 t^{- \frac{1}{2}}$ $R(t)=4/sqrt(16t)=4/(sqrt16xxsqrtt)=4/(4t^(1/2))=1t^(-1/2)$

$(b)$ $(b)$

$T (s) = (6 s^{- 2}) (4 s^{- 3}) = 6 \times 4 \times s^{(- 2 - 3)} = 24 s^{- 5}$ $T(s)=(6s^-2)(4s^-3)=6xx4xxs^((-2-3))=24s^-5$

$(c)$ $(c)$

$K (w) = \frac{w^{4}}{4 \sqrt{w^{3}}} = \frac{w^{4}}{4 w^{\frac{3}{2}}} = \frac{1}{4} w^{(4 - \frac{3}{2})} = \frac{1}{4} w^{\frac{5}{2}}$ $K(w)=(w^4)/(4sqrt(w^3))=(w^4)/(4w^(3/2))=1/4w^((4-3/2))=1/4w^(5/2)$

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Write each of the following functions in the form: f(x)=kx^p?

After I simplified the expression, how would I write the answers in f(x)=kx^p form?

1 Answer

Explanation:

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