Question 11 Mark
Using laws of exponents, simplify and write the answer in exponential form.
$8^t÷8^2$
Answer$8^t \div 8^2=8^{t-2}$ $\left[\because a^m+a^n=a^{m-n}\right]$
View full question & answer→Question 21 Mark
Using laws of exponents, simplify and write the answer in exponential form.
$\left(2^{20}÷2^{15}\right) \times 2^3$
Answer$\left(2^{20} \div 2^{15}\right) \times 2^3=\left(2^{20-15}\right) \times 2^3$
$=2^5 \times 2^3=2^{5+3}=2^8$
View full question & answer→Question 31 Mark
Using laws of exponents, simplify and write the answer in exponential form.
$a^4 \times b^4$
Answer$a^4 \times b^4=(a \times b)^4=(a b)^4$
View full question & answer→Question 41 Mark
Using laws of exponents, simplify and write the answer in exponential form.
$2^5 \times 5^5$
Answer$2^5 \times 5^5=(2 \times 5)^5=10^5$ $\left[\because a^m \times b^m=(a \times b)^m\right]$
View full question & answer→Question 51 Mark
Using laws of exponents, simplify and write the answer in exponential form.
$7^x \times 7^2$
Answer$7^x \times 7^2=7^{x+2}$
View full question & answer→Question 61 Mark
Using laws of exponents, simplify and write the answer in exponential form.
$a^3 \times a^2$
Answer$a^3 \times a^2=a^{3+2}=a^5$
View full question & answer→Question 71 Mark
Put into another form using $a^m+b^m=\left(\frac{a}{b}\right)^m$.
$5^6÷(-2)^6$
Answer$5^6÷(-2)^6=\frac{5^6}{(-2)^6}=\left(\frac{5}{-2}\right)^6=\left(\frac{-5}{2}\right)^6$
View full question & answer→Question 81 Mark
Put into another form using $a^m+b^m=\left(\frac{a}{b}\right)^m$.
$p^4÷q^4$
Answer$p^4 \div q^4=\frac{p^4}{q^4}=\left(\frac{p}{q}\right)^4$
View full question & answer→Question 91 Mark
Put into another form using $a^m+b^m=\left(\frac{a}{b}\right)^m$.
$(-2)^3÷b^3$
Answer$(-2)^3 \div b^3=\frac{(-2)^3}{b^3}=\left(\frac{-2}{b}\right)^3$
View full question & answer→Question 101 Mark
Put into another form using $a^m+b^m=\left(\frac{a}{b}\right)^m$.
$2^5÷b^5$
Answer$2^5 \div b^5=\frac{2^5}{b^5}=\left(\frac{2}{b}\right)^5$
View full question & answer→Question 111 Mark
Put into another form using $a^m+b^m=\left(\frac{a}{b}\right)^m$.
$4^5÷3^5$
Answer$4^5 \div 3^5=\frac{4^5}{3^5}=\left(\frac{4}{3}\right)^5$ $\left[\because a^m \div b^m=\frac{a^m}{b^m}=\left(\frac{a}{b}\right)^m\right]$
View full question & answer→Question 121 Mark
Put into another form using $a^m \times b^m=(a b)^m$.
$5^6 \times(-2)^6$
Answer$5^6 \times(-2)^6=[5 \times(-2)]^6=(-10)^6$
View full question & answer→Question 131 Mark
Put into another form using $a^m \times b^m=(a b)^m$.
$a^2 \times t^2$
Answer$a^2 \times t^2=(a \times t)^2=(a t)^2$
View full question & answer→Question 141 Mark
Put into another form using $a^m \times b^m=(a b)^m$.
$2^5 \times b^5$
Answer$2^5+b^5=\frac{2^5}{b^5}=\left(\frac{2}{b}\right)^5$
View full question & answer→Question 151 Mark
Put into another form using $a^m \times b^m=(a b)^m$.
$4^3 \times 2^3$
Answer$4^3 \times 2^3=(4 \times 2)^3=8^3 \quad\left[\because a^m \times b^m=(a b)^m\right]$
View full question & answer→Question 161 Mark
Simplify and write the answer in exponential form.
$\left(5^3\right)^7$
Answer$\left(5^3\right)^7=5^{3 \times 7}=5^{21}$
View full question & answer→Question 171 Mark
Simplify and write the answer in exponential form.
$\left(7^{50}\right)^2$
Answer$\left(7^{50}\right)^2=7^{50 \times 2}=7^{100}$
View full question & answer→Question 181 Mark
Simplify and write the answer in exponential form.
$\left(2^2\right)^{100}$
Answer $\left(2^2\right)^{100}=2^{2 \times 100}=2^{200}$
View full question & answer→Question 191 Mark
Simplify and write the answer in exponential form.
$\left(6^2\right)^4$
Answer $\left(6^2\right)^4=6^{2 \times 4}=6^8$ $\left[\because\left(a^m\right)^n=a^{m n}\right]$
View full question & answer→Question 201 Mark
Simplify and write in exponential form.
$(-4)^{100} \times(-4)^{20}$
Answer$(-4)^{100} \times(-4)^{20}=(-4)^{100+20}=(-4)^{120}$
View full question & answer→Question 211 Mark
Simplify and write in exponential form.
$5^3 \times 5^7 \times 5^{12}$
Answer$5^3 \times 5^7 \times 5^{12}=5^{3+7} \times 5^{12}=5^{10} \times 5^{12}=5^{10+12}=5^{22}$
View full question & answer→Question 221 Mark
Simplify and write in exponential form.
$a^3 \times a^2 \times a^7$
Answer$a^3 \times a^2 \times a^7=a^{3+2} \times a^7=a^5 \times a^7=a^{5+7}=a^{12}$
View full question & answer→Question 231 Mark
Simplify and write in exponential form.
$4^3 \times 4^2$
Answer$4^3 \times 4^2=4^{3+2}=4^5$
View full question & answer→Question 241 Mark
Simplify and write in exponential form.
$p^3 \times p^2$
Answer$p^3 \times p^2=p^{3+2}=p^5$
View full question & answer→Question 251 Mark
Simplify and write in exponential form.
$2^5 \times 2^3$
Answer$2^5 \times 2^3=2^{5+3}=2^8$ $\left[\because a^m \times a^n=a^{m+n}\right]$
View full question & answer→Question 261 Mark
Compare the following numbers.
$4 \times 10^{14} ; 3 \times 10^{17}$
Answer$3 \times 10^{17}$ is greater than $4 \times 10^{14}$.
View full question & answer→Question 271 Mark
Express each of the following as product of powers of their prime factors.
3603
Answer$2^4 \times 3^2 \times 5^2$
View full question & answer→Question 281 Mark
Express each of the following as product of powers of their prime factors.
540
Answer$2^2 \times 3^3 \times 5$
View full question & answer→Question 291 Mark
Express each of the following as product of powers of their prime factors.
405
Question 301 Mark
Identify the greater number, wherever possible, in each of the following?
$2^{10}$ or $10^2$
Answer$2^{10}$ is greater than $10^2$.
View full question & answer→Question 311 Mark
Identify the greater number, wherever possible, in each of the following?
$100^2$ or $2^{100}$
Answer$2^{100}$ is greater than $100^2$.
View full question & answer→Question 321 Mark
Identify the greater number, wherever possible, in each of the following?
$2^8$ or $8^2$
Answer$2^{\text {8 }}$ is greater than $8^2$.
View full question & answer→Question 331 Mark
Identify the greater number, wherever possible, in each of the following?
$5^3$ or $3^5$
Answer$3^3$ is greater than $5^3$.
View full question & answer→Question 341 Mark
Express the following in exponential form.
a × a × a × c × c × c × c × d
Answer$a \times a \times a \times c \times c \times c \times c \times d=a^3 \times c^4 \times d$
View full question & answer→Question 351 Mark
Express the following in exponential form.
2 × 2 × a × a
Answer$2 \times 2 \times a \times a=2^2 \times a^2$
View full question & answer→Question 361 Mark
Express the following in exponential form.
5 × 5 × 7 × 7 × 7
Answer$5 \times 5 \times 7 \times 7 \times 7=5^2 \times 7^3$
View full question & answer→Question 371 Mark
Express the following in exponential form.
b × b × b × b
Answer$b \times b \times b \times b=b^4$
View full question & answer→Question 381 Mark
Express the following in exponential form.
t × t
Question 391 Mark
Express the following in exponential form.
6 × 6 × 6 × 6
Answer$6 \times 6 \times 6 \times 6=6^4$
View full question & answer→Question 401 Mark
Find the value of:
$5^4$
Answer$5^4=5 \times 5 \times 5 \times 5=625$. Hence, the value of $5^4$ is 625.
View full question & answer→Question 411 Mark
Find the value of:
$11^2$
Answer$11^2=11 \times 11=121$. Hence, the value of $11^2$ is 121.
View full question & answer→Question 421 Mark
Find the value of:
$9^3$
Answer$9^3=9 \times 9 \times 9=729$. Hence, the value of $9^3$ is 729.
View full question & answer→Question 431 Mark
Find the number from each of the following expanded forms.
$9 \times 10^5+2 \times 10^2+3 \times 10^1$
View full question & answer→Question 441 Mark
Find the number from each of the following expanded forms.
$3 \times 10^4+7 \times 10^2+5 \times 10^0$
View full question & answer→Question 451 Mark
Express each of the following as a product of prime factors only in exponential form.
768
Question 461 Mark
Express each of the following as a product of prime factors only in exponential form.
$729 \times 64$
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