# Exponenets

1. Given that $(1/x)2 = 0.04,$ find the value of $x.$

(A)   1/5
(B)   1/2
(C)   5
(D)   10

Correct: C
$(1/5)^2 = 1/25 = 0.04$

2.  Given that $3^{x - 1} = 243,$ find the value of $x.$

(A)   4
(B)   5
(C)   6
(D)   82

Correct: C

$3^{(6 - 1)} = 3^5 = 243$

3. If $x + 121,121 = 121,121,121,$ then $x =$

(A)   $1.21 \times 10^9$
(B)   $1.21 \times 10^8$
(C)   $1.21 \times 10^7$
(D)   $1.21 \times 10^6$

Correct: B
$121.000.000 + 121.121 = 121.121.121 \\ = 1.21 \times 10^8 + 121.121$

4. Evaluate  $\frac{250 \times 10^{-6}}{10^3}$, writing your answer in standard form.

(A)   $2.5 \times 10^{-1}$
(B)   $2.5 \times 10^{-7}$
(C)   $2.5 \times 10^{-9}$
(D)   $2.5 \times 10^{-11}$

Correct: B
$2.50 \times 10^{-7}$

5.  The value of $4^3 \times 16^3$ is:

(A)   $64^6$
(B)   $8^6$
(C)   $4^8$
(D)   $2^{13}$

Correct: B
$4^3 \times 16^3 = \\ 4^3 \times (4^2)^3 = \\ 4^3 + 2 · 3 = \\ 4^3 + 6 = 4^9 \\ 4^9 = 8^6$

Thanks to Suparna Roy I can now supply the last part of the explanation:

$4^9 = (2^2)^9 = 2^{18} = (2^3)^6 = 8^6$

6.  Simplify  : $[p^{-7}\div p^{-3} \times p^4 ]^2$

(A)   $p^{-36}$
(B)   $p^{-12}$
(C)   $0$
(D)   $1$

Correct: D
$[p^{-7}\div p^{-3} \times p^4 ]^2\quad\text{rewritten is} \\ = (p^{-7}/p^{-3} \times p^4)^2 \\ = (p^{-7} + 3 \times p^4)^2 \\ = (p^{-4} \times p^4) \\ = p^{-4} + 4 \\ = p^0 = 1$

7.  Simplify: $\bigg[ \frac{p^{-3}\times p^7}{p^{-10}\times p^3} \bigg]$

(A)   $p^{-6}$
(B)   $p^{11}$
(C)   $p^{22}$
(D)   $p^{121}$

Correct: C
$\bigg[ \frac{p^{-3}\times p^7}{p^{-10}\times p^3} \bigg] \\ = (p^{-3} \times p^7)^2 - (p^{-10} \times p^3)^2 \\ = (p^4)^2 - (p^{-7})^2 \\ = p^8 - p^{-14} \\ = p^{8 + 14} = p^{22} \\$

8. $(7m^2n^2) \cdot (4m^3n^2) =$

(A)   $11\;m^5n^4$
(B)   $28\; m^5n^4$
(C)   $28\;m^6n^4$
(D)   $28\;m^{23}n^{22}$

Correct: B
$(7\;m^2n^2) · (4\;m^3n^2) \\ = (4 \times 7)·(m^{2 + 3})·(n^{2 + 2}) \\ = 28\;m^5n^4$

9. $(9ax^2) \cdot (8xy^2) =$

(A)   $36\;axy^3$
(B)   $72\;ax^2y^2$
(C)   $72\;ax^3y^2$
(D)   $98\;ax^2y^2$

Correct: C
$(9\;ax^2)·(8\;xy^2) \\ = (9 \times 8)·(ay^2x^{2 + 1}),br> = 72\;ax^3y^2$

10.  $\frac{(a^5)^{10}}{a^5}=$

(A)   $a^{50}$
(B)   $a^{45}$
(C)   $a^{15}$
(D)   $a^{10}$

$a^{45}$