Surds and Indices Quiz Set 008

Question 1

What is \$({2/9})^{x - 0.05} × ({2/9})^x = ({2/9})^2.3\$?

A

1.175.

B

1.675.

C

2.675.

D

3.175.

Soln.
Ans: a

We can simplify the given expression to \$({2/9})^{2x - 0.05} = ({2/9})^2.3\$. The bases are equal, so the powers should also be equal. Hence \$2x - 0.05 = 2.3\$ which gives x = 1.175.

Question 2

If \$p^q = 5\$, then what could be \$(p - 1)^(q + 1)\$?

A

16.

B

17.

C

15.

D

18.

Soln.
Ans: a

By inspection we can see that p = 5, q= 1. So \$(5 - 1)^(1 + 1)\$ will be \$4^2\$, i.e., 16.

Question 3

If \$√86\$ is approximately \$9\$, then what is \$86^3\$?

A

531441.

B

531442.

C

531440.

D

531443.

Soln.
Ans: a

Since \$√x = x^{1/2}\$, we can see that \$86^3\$ is same as \$(√86)^6\$ which gives \$9^6\$ = 531441.

Question 4

What is \$({11/12})^{x - 0.27} × ({11/12})^x = ({11/12})^0.32\$?

A

0.295.

B

0.795.

C

1.795.

D

2.295.

Soln.
Ans: a

We can simplify the given expression to \$({11/12})^{2x - 0.27} = ({11/12})^0.32\$. The bases are equal, so the powers should also be equal. Hence \$2x - 0.27 = 0.32\$ which gives x = 0.295.

Question 5

What is \$31^3.1 × 31^x = 31^1.8\$?

A

-1.3.

B

-0.8.

C

0.2.

D

0.7.

Soln.
Ans: a

We can simplify the given expression to \$31^{3.1 + x} = 31^1.8\$. The bases are equal, so the powers should also be equal. Hence \$3.1 + x = 1.8\$ which gives x = -1.3. This Blog Post/Article "Surds and Indices Quiz Set 008" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2019-08-18.