44474.If $\sqrt{2^{n}}=64$ then the value of n is:
2
4
6
12
Explanation:
$\sqrt{2^{n}}=64$
$\Leftrightarrow \left(2^{n}\right)^{\dfrac{1}{2}}$ $=2^{6}$
$\Leftrightarrow 2^{\dfrac{n}{2}}=2^{6}$
$\Leftrightarrow \dfrac{n}{2}=6$
$\Leftrightarrow n=12$
$\sqrt{2^{n}}=64$
$\Leftrightarrow \left(2^{n}\right)^{\dfrac{1}{2}}$ $=2^{6}$
$\Leftrightarrow 2^{\dfrac{n}{2}}=2^{6}$
$\Leftrightarrow \dfrac{n}{2}=6$
$\Leftrightarrow n=12$
44475.If $5\sqrt{5}\times 5^{3}+5^{-\dfrac{3}{2}}$ $=5^{a+2}$, then the value of a is:
4
5
6
8
Explanation:
$5\sqrt{5}\times 5^{3}+5^{-\dfrac{3}{2}}$ $=5^{a+2}$
$\Leftrightarrow \dfrac{5 \times 5^{\dfrac{1}{2}} \times 5^{3}}{5^{-\dfrac{3}{2}}}=5^{a+2}$
$\Leftrightarrow 5^{\left(1+\dfrac{1}{2}+3+\dfrac{3}{2}\right)}$ $=5^{a+2}$
$\Leftrightarrow 5^{6}$ $=5^{a+2}$
$\Leftrightarrow a+2=6$
$\Leftrightarrow a=4$
$5\sqrt{5}\times 5^{3}+5^{-\dfrac{3}{2}}$ $=5^{a+2}$
$\Leftrightarrow \dfrac{5 \times 5^{\dfrac{1}{2}} \times 5^{3}}{5^{-\dfrac{3}{2}}}=5^{a+2}$
$\Leftrightarrow 5^{\left(1+\dfrac{1}{2}+3+\dfrac{3}{2}\right)}$ $=5^{a+2}$
$\Leftrightarrow 5^{6}$ $=5^{a+2}$
$\Leftrightarrow a+2=6$
$\Leftrightarrow a=4$
44476.If $2^{2n-1}=\dfrac{1}{8^{n-3}}$, then the value of n is:
3
2
0
-2
Explanation:
$2^{2n-1}=\dfrac{1}{8^{n-3}}$
$\Leftrightarrow 2^{2n-1}=\dfrac{1}{\left(2^{3}\right)^{n-3}}$
$\Leftrightarrow 2^{2n-1}=\dfrac{1}{2^{3}\left(^{n-3}\right)}$
$\Leftrightarrow 2^{2n-1}=\dfrac{1}{2\left(^{3n-9}\right)}$ $=2^\left({9-3n}\right)$
$\Leftrightarrow 2n-1$ $=9-3n$
$\Leftrightarrow 5n=10$
$\Leftrightarrow n=2$
$2^{2n-1}=\dfrac{1}{8^{n-3}}$
$\Leftrightarrow 2^{2n-1}=\dfrac{1}{\left(2^{3}\right)^{n-3}}$
$\Leftrightarrow 2^{2n-1}=\dfrac{1}{2^{3}\left(^{n-3}\right)}$
$\Leftrightarrow 2^{2n-1}=\dfrac{1}{2\left(^{3n-9}\right)}$ $=2^\left({9-3n}\right)$
$\Leftrightarrow 2n-1$ $=9-3n$
$\Leftrightarrow 5n=10$
$\Leftrightarrow n=2$
44477.If a and b are whole numbers such that ab = 121, then find the value of (a – 1)b+1
0
10
102
103
Explanation:
121 = 112, hence value of a = 11 and b = 2 can be considered.
Therefore, the value of (a – 1)b+1 = (11 – 1)2+1= 103
121 = 112, hence value of a = 11 and b = 2 can be considered.
Therefore, the value of (a – 1)b+1 = (11 – 1)2+1= 103
44478.$(1000)^{7}\div 10^{18}=?$
10
100
1000
10000
Explanation:
$(1000)^{7}\div 10^{18}$
$=\dfrac{(1000)^{7}}{10^{18}}$
$=\dfrac{10^{(3 \times 7)}}{10^{18}}$
$=\dfrac{10^{21}}{10^{18}}$
$=(10)^{(21-18)}$
$=10^{3}=1000$
$(1000)^{7}\div 10^{18}$
$=\dfrac{(1000)^{7}}{10^{18}}$
$=\dfrac{10^{(3 \times 7)}}{10^{18}}$
$=\dfrac{10^{21}}{10^{18}}$
$=(10)^{(21-18)}$
$=10^{3}=1000$
44479.$(2.4 \times 10^{3})\div (8 \times 10^{-2})=?$
$(3 \times 10^{-5})$
$(3 \times 10^{4})$
$(3 \times 10^{5})$
30
Explanation:
$=(2.4 \times 10^{3})\div (8 \times 10^{-2})$
$=\dfrac{24 \times 10^{2}}{8 \times 10^{-2}}$
$=(3\times 10^{4})$
44480.The value of $\dfrac{1}{(216)^{-\dfrac{2}{3}}}$ $ +\dfrac{1}{(256)^{-\dfrac{3}{4}}}$ $+\dfrac{1}{(32)^{-\dfrac{1}{5}}}$ is :
102
105
107
109
Explanation:
$\dfrac{1}{(216)^{-\dfrac{2}{3}}}$ $ +\dfrac{1}{(256)^{-\dfrac{3}{4}}}$ $+\dfrac{1}{(32)^{-\dfrac{1}{5}}}$
$=\dfrac{1}{(6^{3})^{-\dfrac{2}{3}}}$ $ +\dfrac{1}{(4^{4})^{\left(-\dfrac{3}{4}\right)}}$ $+\dfrac{1}{(2^{5})^{-\dfrac{1}{5}}}$
$=\dfrac{1}{6^{3} \times \dfrac{(-2)}{3}}$ $+\dfrac{1}{4^{4}\times \dfrac{(-3)}{4}}$ $+\dfrac{1}{2^{5} \times \dfrac{-1}{5}}$
$=\dfrac{1}{6^{-2}}$ $+\dfrac{1}{4^{-3}}$ $+\dfrac{1}{2^{-1}}$
$=6^{2}+4^{3}+2^{1}$
$=(36+64+2)=102$
44482.The value of 51/4 * (125)0.25 is:
√5
5√5
5
25
Explanation:
50.25* (53)0.25
50.25* 50.75
= 51
= 5.
50.25* (53)0.25
50.25* 50.75
= 51
= 5.
44483.The value of (32/243)-4/5is:
4/9
9/4
16/81
81/16
Explanation:
(32/243)-4/5
= (243/32)4/5
= [(3/2)5]4/5
= 81/16
(32/243)-4/5
= (243/32)4/5
= [(3/2)5]4/5
= 81/16