Question 12 Marks
Simplify and express the following in exponential form:
$\Big({\frac{5}{2}}\Big)^6\times\Big(\frac{5}{2}\Big)^2$
Answer$\Big({\frac{5}{2}}\Big)^6\times\Big(\frac{5}{2}\Big)^2$
We know that,
$\left(a^m \times a^n\right)=(a)^{m+n}$
Here, $\text{a}=\frac{5}{2}$
$=\Big(\frac{5}{2}\Big)^{6+2}$
$=\Big(\frac{5}{2}\Big)^8$
View full question & answer→Question 22 Marks
Using laws of exponents, simplify and write the answer in exponential form:
$5^{12} \div 2^3$
Answer$5^{12} \div 2^3$
We know that, $a^m \div a^n=a^{m-n}$
So,
$5^{12} \div 5^3=5^{12-3}$
$=5^9$
View full question & answer→Question 32 Marks
Simplify and express the following in exponential form:
$\Big({\frac{2}{3}}\Big)^5\times\Big(\frac{3}{5}\Big)^5$
Answer$\Big({\frac{2}{3}}\Big)^5\times\Big(\frac{3}{5}\Big)^5$
We know that, $\left(a^m \times b^m\right)=(a \times b)^m$
$=\Big(\frac{2}{3}\times\frac{3}{5}\Big)^5$
$=\Big(\frac{2}{5}\Big)^5$
View full question & answer→Question 42 Marks
Simplify and write the following in exponential form:
$(81)^5 \div\left(3^2\right)^5$
Answer$(81)^5 \div\left(3^2\right)^5$
$=(34)^5 \div(32)^5$
$=3^{20} \div 3^{10}$
$=3^{20-10}$
$=3^{10}$
View full question & answer→Question 52 Marks
Find the values of n in the following:
$\Big(\frac{3}{2}\Big)^4\times\Big(\frac{3}{2}\Big)^5=\Big(\frac{3}{2}\Big)^{2\text{n}+1}$
Answer$\Big(\frac{3}{2}\Big)^4\times\Big(\frac{3}{2}\Big)^5=\Big(\frac{3}{2}\Big)^{2\text{n}+1}$
$=\Big(\frac{3}{2}\Big)^{(4+5)}=\Big(\frac{3}{2}\Big)^{(2\text{n}+1)}$
Equating the powers
$=4+5=2\text{n}+1$
$=2\text{n}+1=9$
$=2\text{n}=8$
$=\text{n}=4$
View full question & answer→Question 62 Marks
Find the number from the following expanded forms:
$9 \times 10^5+5 \times 10^2+3 \times 10^1$
AnswerWe have:
$9 \times 10^5+5 \times 10^2+3 \times 10^1$
$=9 \times 100000+5 \times 100+3 \times 10=900530$
View full question & answer→Question 72 Marks
Simplify and express the following in exponential form:
$\Big(\frac{\text{x}}{\text{y}}\Big)^{12}\times\text{y}^{24}\times(2^3)^4$
Answer$\Big(\frac{\text{x}}{\text{y}}\Big)^{12}\times\text{y}^{24}\times(2^3)^4$
$=\Big(\frac{\text{x}^{12}}{\text{y}^{12}}\Big)\times\text{y}^{24}\times2^{12}$
$=\text{x}^{12}\times\text{y}^{24-12}\times2^{12}$
$=\text{x}^{12}\times\text{y}^{12}\times2^{12}$
$=(2\text{xy})^{12}$
View full question & answer→Question 82 Marks
Using laws of exponents, simplify and write the answer in exponential form:
$\left(5^{21} \div 5^{13}\right) \times 5^7$
Answer$\left(5^{21} \div 5^{13}\right) \times 5^7$
We know that,
$a^m \div a^n=a^{m-n} \text { and }\left(a^m \times a^n\right)=(a)^{m+n}$
$\text { So, }\left(5^{21} \div 5^{13}\right) \times 5^7=\left(5^{21-13}\right) \times 5^7$
$=\left(5^8\right) \times 5^7$
$=5^{8+7}$
$=5^{15}$
View full question & answer→Question 92 Marks
Simplify and write the following in exponential form:
$(25)^3 \div 5^3$
Answer$(25)^3 \div 5^3$
$=\left(5^2\right)^3 \div 5^3$
$=5^6 \div 5^3$
$=5^{6-3}$
$=5^3$
View full question & answer→Question 102 Marks
Simplify and express the following in exponential form:
$\left\{\left(2^3\right)^4 \times 2^8\right\}+2^{12}$
Answer$\left\{\left(2^3\right)^4 \times 2^8\right\} \div 2^{12}$
$=\left\{\left(2^{12} \times 2^8\right\} \div 2^{12}\right.$
$=2^{(12+8)} \div 2^{12}$
$=2^{20} \div 2^{12}$
$=2^{(20-12)}=2^8$
View full question & answer→Question 112 Marks
Find the values of n in the following:
$9 \times 3^n=3^7$
Answer$9 \times 3^n=3^7$
$\Rightarrow(3)^2 \times 3^n=3^7$
$\Rightarrow(3)^{2+n}=3^7$
Equating the powers
$\Rightarrow 2+n=7$
$\Rightarrow n=7-2$
$\Rightarrow n=5$
View full question & answer→Question 122 Marks
Using laws of exponents, simplify and write the answer in exponential form:
$\left(7^2\right)^3$
Answer$\left(7^2\right)^3$
We know that, $\left(a^m\right)^n=a^{m n}$
So,$\left(7^2\right)^3=7^{(2)(3)}$
$=7^6$
View full question & answer→Question 132 Marks
Using laws of exponents, simplify and write the answer in exponential form:
$3^7 \times 2^7$
Answer$3^7 \times 2^7$
We know that $\left(a^m \times b^m\right)=(a \times b)^m$
So,
$3^7 \times 2^7=(3 \times 2)^7$
$=6^7$
View full question & answer→Question 142 Marks
Find the values of n in the following:
$7^{2 n+1} \div 49=7^3$
Answer$7^{2 n+1} \div 49=7^3$
$=7^{2 n+1} \div 7^2=7^3$
$=7^{2 n+1-2}=7^3$
$=7^{2 n-1}=7^3$
Equating the powers
$=2 n-1=3$
$=2 n=4$
$=n=2$
View full question & answer→Question 152 Marks
Find the number from the following expanded forms:
$7 \times 10^4+6 \times 10^3+0 \times 10^2+4 \times 10^1+5 \times 10^0$
AnswerWe have:
$7 \times 10^4+6 \times 10^3+0 \times 10^2+4 \times 10^1+5 \times 10^0$
$=7 \times 10000+6 \times 1000+0 \times 100+4 \times 10+5 \times 1$
$=76045$
View full question & answer→Question 162 Marks
Using laws of exponents, simplify and write the answer in exponential form:
$\left(3^2\right)^5 \div 3^4$
Answer$\left(3^2\right)^5 \div 3^4$
We know that, $a^m \div a^n=a^{m-n}$ and $\left(a^m\right)^n=a^{m n}$
$\text { So, }\left(3^2\right)^5 \div 3^4=3^{10} \div 3^4$
$=3^{10-4}$
$=3^6$
View full question & answer→Question 172 Marks
Find the values of n in the following:
$8 \times 2^{n+2}=32$
Answer$8 \times 2^{n+2}=32$
$=(2)^3 \times 2^{n+2}=(2)^5$
$=(2)^{3+n+2}=(2)^5$
$=2^{n+5}=2^5$
Equating the powers
$=n+5=5$
$=n=0$
View full question & answer→Question 182 Marks
Find the number from the following expanded forms:
$5 \times 10^5+4 \times 10^4+2 \times 10^3+3 \times 10^0$
AnswerWe have:
$5 \times 10^5+4 \times 10^4+2 \times 10^3+3 \times 10^0$
$=5 \times 100000+4 \times 10000+2 \times 1000+3 \times 1$
$=542003$
View full question & answer→Question 192 Marks
Simplify and express the following in exponential form:
$\frac{5^4\times\text{x}^{10}\text{y}^5}{5^4\times\text{x}^7\text{y}^4}$
Answer$\frac{5^4\times\text{x}^{10}\text{y}^5}{5^4\times\text{x}^7\text{y}^4}$
$=5^{4-4}\times\text{x}^{10-7}\times\text{y}^{5-4}$
$=5^{0}\times\text{x}^3\times\text{y}^1$
$=1\times\text{x}^3\times\text{y}$
$=\text{x}^3\text{y}$
View full question & answer→Question 202 Marks
Using laws of exponents, simplify and write the answer in exponential form:
$2^3 \times 2^4 \times 2^5$
Answer$2^3 \times 2^4 \times 2^5$
We know that,
$a^m+a^n+a^p=a^{m+n+p}$
So, $2^3 \times 2^4 \times 2^5 \times 2^{5+4+5}$
$=2^{12}$
View full question & answer→Question 212 Marks
Simplify and express the following in exponential form:
$\left\{\left(3^2\right)^3 \times 2^6\right\} \times 5^6$
Answer$\quad\left\{\left(3^2\right)^3 \times 2^6\right\} \times 5^6$
$=\left(3^6 \times 2^6\right) \times 5^6$
$=6^6 \times 5^6$
$=30^6$
View full question & answer→Question 222 Marks
Find the values of n in the following:
$5^{2 n} \times 5^3=5^{11}$
Answer$\quad 5^{2 n} \times 5^3=5^{11}$
$5^{2 n+3}=5^{11}$
Equating the powers
$2 n+3=11$
$\Rightarrow 2 n=11-3$
$\Rightarrow 2 n=8$
$n=4$
View full question & answer→Question 232 Marks
Simplify and express the following in exponential form:
$\left(8^2 \times 8^4\right) \div 8^3$
Answer$\left(8^2 \times 8^4\right) \div 8^3$
$=8^{(2+4)} \div 8^3$
$=8^6 \div 8^3$
$=8^{(6-3)}=8^3=\left(2^3\right)^3=2^9$
View full question & answer→Question 242 Marks
Simplify and express the following in exponential form:
$\Big(\frac{5^7}{5^2}\Big)\times5^3$
Answer$\Big(\frac{5^7}{5^2}\Big)\times5^3$
$=5^{7-2}\times5^3$
$=5^5\times5^3$
$=5^{5+3}$
$=5^{8}$
View full question & answer→