What is (x-5)^{7/2}-25(x-5)^{3/2} ?

The solution to (x-5)^{7/2}-25(x-5)^{3/2} is (x-5)^3(x-5)^{1/2}-25(x-5)(x-5)^{1/2}

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(x-5)^{7/2}-25(x-5)^{3/2}

(x - 5)^{\frac{7}{2}} - 25 (x - 5)^{\frac{3}{2}}

(x - 5)^{3} (x - 5)^{\frac{1}{2}} - 25 (x - 5) (x - 5)^{\frac{1}{2}}

Solution steps

(x - 5)^{\frac{7}{2}} - 25 (x - 5)^{\frac{3}{2}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x - 5)^{\frac{7}{2}} = (x - 5)^{3 + \frac{1}{2}} = (x - 5)^{3} (x - 5)^{\frac{1}{2}}

= (x - 5)^{3} (x - 5)^{\frac{1}{2}} - 25 (x - 5)^{\frac{3}{2}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x - 5)^{\frac{3}{2}} = (x - 5)^{1 + \frac{1}{2}} = (x - 5) (x - 5)^{\frac{1}{2}}

= (x - 5)^{3} (x - 5)^{\frac{1}{2}} - 25 (x - 5) (x - 5)^{\frac{1}{2}}

\frac{6}{7} = 9 m

ln (3) \cdot ln (3)

\frac{135 π}{180}

3 (\frac{1}{9})

(\frac{1}{4} m - 2 n)^{2}

What is (x-5)^{7/2}-25(x-5)^{3/2} ?
The solution to (x-5)^{7/2}-25(x-5)^{3/2} is (x-5)^3(x-5)^{1/2}-25(x-5)(x-5)^{1/2}