Test Index

Powers and Roots Practice Test 5

© examsnet.com

Question : 15 of 31

Marks: +1, -0

Find x in:

(169)^{3} \times 13 \div (2,197)^{2} = (13)^{x} .

3
1
-1
2
4

Solution:

Concept:

Write all numbers as powers of

13

, then use exponent laws to compare powers.

Explanation:

Given:

(169)^3 \times 13 \div (2197)^2 = (13)^x

.

Now,

169 = 13^2

and

2197 = 13^3

.

So,

(13^2)^3 \times 13 \div (13^3)^2 = (13)^x

.

Using

(a^m)^n = a^{mn}

:

13^6 \times 13^1 \div 13^6 = (13)^x

.

Using

a^m \times a^n = a^{m+n}

and

a^m \div a^n = a^{m-n}

:

13^{6+1-6} = (13)^x

.

Thus,

13^1 = 13^x

.

Comparing powers gives

x = 1

.

Answer:

x = 1

, which matches option B.

© examsnet.com

Go to Question:

Prev Question

Next Question