Surds and Indices Quiz Set 012

Question 1

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

A

6.

B

10.

C

14.

D

18.

Soln.
Ans: a

Simplifying, we get \$(5^4)^1.5 × 5^5\$ ÷ \$(5 ^ 2)^2.5\$ = \$5^x\$, which simplifies to \$5^6 × 5^5\$ ÷ \$5^5\$ = \$5^x.\$ Equating the powers x = 6 + 5 - 5 = 6.

Question 2

What is \$16^0.15 × 16^0.1\$?

A

2.

B

3.

C

5.

D

4.

Soln.
Ans: a

By inspection, we get \$(2^4)^0.15 × (2^4)^0.1\$, which equals \$(2^4)^(0.15 + 0.1)\$, which equals \$(2^4)^0.25\$, which equals \$2^1\$, or 2. Note: The trick in such type of questions is to keep an eye on the "bases".

Question 3

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

A

243.

B

244.

C

242.

D

245.

Soln.
Ans: a

We can write the given expression as \$3^x = 3^6\$. The bases are same so powers should be same. Comparing we get x = 6. So x - 1 = 5, we get \$3^5 = 243\$.

Question 4

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

A

-0.00999999999999998.

B

0.49.

C

1.49.

D

1.99.

Soln.
Ans: a

We can simplify the given expression to \$({19/28})^{0.12 + x} = ({19/28})^0.11\$. The bases are equal, so the powers should also be equal. Hence \$0.12 + x = 0.11\$ which gives x = -0.00999999999999998.

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".