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### Question 1

What is the value of x if $(625)^1.5 × 5^5$ ÷ $25^2.5$ = $5^x$?

### Question 2

What is $16^0.15 × 16^0.1$?

### Question 3

If $3^x = 729$, then what is the value of $3^{x - 1}$?

### Question 4

What is $({19/28})^0.12 × ({19/28})^x = ({19/28})^0.11$?

### Question 5

If $2^{m + n} = 32$, and $2^{m - n} = 4$, then what is m?

**A**

3.5.

**B**

4.0.

**C**

5.0.

**D**

6.0.

**Soln.**

**Ans: a**

By inspection, both the expressions can be simplified to $2^{m + n} = 2^5$ and $2^{m - n} = 2^2$. The bases are same, so powers should be same as well. So these expressions lead us to two simultaneous equations $m + n = 5$ and $m - n = 2$. Solving, we get $m = {5 + 2}/2$ = 3.5. Note: The trick in such type of questions is to keep an eye on the "bases".

This Blog Post/Article "Surds and Indices Quiz Set 012" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2017-04-07.