If 5\sqrt5\times5^3\div5^{-3/2}=5^{a+2}, then find the value of a.

Surds and Indices Practice Test 1

Question : 4 of 40

Marks: +1, -0

5√5×5^3÷5^{-3/2}=5^{a+2}

, then find the value of a.

Solution:

5√5×5^3÷5^{-3/2}=5^{a+2}

⇒5^{3/2}×5^3÷5^{-3/2}=5^{a+2}

⇒5^{(3/2+3+3/2)}=5^{a+2}

⇒5^6=5^{a+2}

⇒6=a+2

⇒a=4

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