Test Index

Surds and Indices Practice Test 1

© examsnet.com

Question : 4 of 40

Marks: +1, -0

If

5\sqrt{5} \times 5^{3} \div 5^{-3/2} = 5^{a+2}

, then find the value of a.

8
6
5
4

Solution:

Concept:

Use exponent laws to combine powers with the same base.

Explanation:

Write

5\sqrt{5}

as a power of

5

:

5\sqrt{5}=5^1 \cdot 5^{1/2}=5^{3/2}

.

Now simplify the left side:

5^{3/2}\times 5^{3}\div 5^{-3/2}=5^{3/2+3-(-3/2)}

=5^{3/2+3+3/2}=5^{6}

So,

5^{6}=5^{a+2}

.

Since bases are equal, equate exponents:

6=a+2

.

Thus,

a=6-2=4

.

Answer:

a=4

© examsnet.com

Go to Question:

Prev Question

Next Question