Surds And Indices

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  1. a0 = 1
  2. a-m = 1/am
  3. (am)n = amn
  4. am / an = am-n
  5. am x b= (ab)m
  6. am / b= (a/b)m
  7. (a/b)-m = (b/a)m
  8. (1)n = 1 for infinite values of n.

1 $$\frac{{{{\left( {243} \right)}^{n/5}} \times {3^{2n + 1}}}}{{{9^n} \times {3^{n - 1}}}} = ?$$

A
1
B
2
C
9
D
3n

2 $$\frac{1}{{1 + {a^{\left( {n - m} \right)}}}} + \frac{1}{{1 + {a^{\left( {m - n} \right)}}}} = ?$$

A
0
B
$$\frac{1}{2}$$
C
1
D
am + n

3 If m and n are whole numbers such that mn = 121, the value of (m - 1)n + 1 is:

A
1
B
10
C
121
D
1000

4 $${\left( {\frac{{{x^b}}}{{{x^c}}}} \right)^{\left( {b + c - a} \right)}}.$$   $${\left( {\frac{{{x^c}}}{{{x^a}}}} \right)^{\left( {c + a - b} \right)}}.$$   $${\left( {\frac{{{x^a}}}{{{x^b}}}} \right)^{\left( {a + b - c} \right)}}$$   = ?

A
xabc
B
1
C
xab + bc + ca
D
xa + b + c

5 If $$x = 3 + 2\sqrt 2 ,$$    then the value of $$\left( {\sqrt x - \frac{1}{{\sqrt x }}} \right)$$   is:

A
1
B
2
C
$$2\sqrt 2 $$
D
$$3\sqrt 3 $$

6 Simplify : (3)8 × (3)4 = ?

A
(27)3
B
(27)5
C
(729)2
D
(729)3

7 Simplify : $$\frac{{343 \times 49}}{{216 \times 16 \times 81}} = ?$$

A
$$\frac{{{7^5}}}{{{6^7}}}$$
B
$$\frac{{{7^5}}}{{{6^8}}}$$
C
$$\frac{{{7^6}}}{{{6^7}}}$$
D
$$\frac{{{7^4}}}{{{6^8}}}$$

8 Simplify : $$\frac{{16 \times 32}}{{9 \times 27 \times 81}} = ?$$

A
$${\left( {\frac{2}{3}} \right)^9}$$
B
$${\left( {\frac{2}{3}} \right)^{11}}$$
C
$${\left( {\frac{2}{3}} \right)^{12}}$$
D
$${\left( {\frac{2}{3}} \right)^{13}}$$

9 Given $$\sqrt 2 $$ = 1.414, the value of $$\sqrt 8 $$ $$\, + $$ $${\text{2}}\sqrt {32} $$ $$\, - $$ $$3\sqrt {128} $$ $$\,\, + $$ $${\text{4}}\sqrt {50} $$  is = ?

A
8.484
B
8.526
C
8.426
D
8.876

10 $${9^3} \times {\left( {81} \right)^2} \div {\left( {27} \right)^3} = {\left( 3 \right)^?}$$

A
3
B
4
C
5
D
6