Product Law

Q. Express $8^{-4}$ as a power with the base 2.

1. $2^{-6}$
2. $2^{-8}$
3. $2^{-12}$
4. $2^{-4}$

Q.

Simplify :$2^{30}+2^{30}+2^{30}+2^{30}$

Q. What will be the product of $p^2-2pq$ and $q^2+5pq$?

1. $pq(4p^2-3q^2+11pq)$
2. $pq(4p^2+3q^2+11pq)$
3. $pq(4p^2-3q^2-11pq)$
4. $pq(5p^2-2q^2-9pq)$

Q. Question 4(ii)
Evaluate:
$(5^{-1}\times 2^{-1})\times 6^{-1}$

Q. $\text{The approximate value of}\sqrt{51}\text{to nearest}$
$\text{tenths is}$

1. 7.5
2. 7.1
3. 7.2
4. 7.3

Q.

Question 4(i)
Evaluate:

$\frac{8^{-1}\times 5^3}{2^{-4}}$

Q.

Question 6(ii)
Evaluate:
${\left(\frac{5}{8}\right)}^{-7}\times {\left(\frac{8}{5}\right)}^{-4}$

Q.

Simplify and express each of the following in exponential form: $\frac{(2^8\times a^5)}{(4^3\times a^3)}$

Q.

(x)^(-a) x (x)^(-b) = ___

1. (x)^(-{a +b})

2. (x)^(-a +b)

3. (x)^(a -b)

4. (x)^(a/b)

Q. Multiplicative inverse of 1 is

1. 0.1
2. 0
3. -1
4. 1

Q.

Simplify :$\left({\left(2^5\right)}^2\times 7^3\right)/\left(8^3\times 7\right)$

Q. The mass of an armored tank is $6\times {10}^4\text{kg}$ and of an armored car is $4\times {10}^3\text{kg}.$ What is the combined weight of both the vehicles?

1. ${10}^5\text{kg}$
2. $6.4\times {10}^5\text{kg}$
3. $6.4\times {10}^4\text{kg}$
4. $4.6\times {10}^4\text{kg}$

Q.

Question 7(ii)
Simplify:
$\frac{3^{-5}\times {10}^{-5}\times 125}{5^{-7}\times 6^{-5}}$

Q. If $\frac{3^{2x-8}}{225}=\frac{5^3}{5^x}$, then $x=$

1. $3$
2. $5$
3. $4$
4. $2$

Q. Find the value of $m$ if $(2{)}^2\times (-5{)}^4={50}^m.$

1. -2
2. 2
3. -4
4. 4

Q.

$\text{Simplify}\frac{(-3{)}^3\times (-3{)}^7}{3\times 9^6}$

1. 27

2. $\frac{1}{27}$

3. $\frac{2}{3}$

4. $\frac{1}{6}$

Q. If $\frac{2^m\times 2^4\times 2^{-6}}{2^{-5}}=2^{10}$, then $m$ = ___.

1. -3
2. 10
3. 7
4. 17

Q.

Question 180(i)

Simplify

${[{\left(\frac{1}{2}\right)}^2-{\left(\frac{1}{4}\right)}^3]}^{-1}\times 2^{-3}$

Q. Simplify :

$\frac{\left(2^{2\times 3}\right)\times (2^{3\times 4})}{2^{20}}$

Q.

Question 180(v)

Simplify

$\frac{(9{)}^3\times 27\times t^4}{(3{)}^{-2}\times (3{)}^4\times t^2}$

Q. Simplify: $x^2\times y^2\times x^5\times y^3$

1. $x^7{y}^5$
2. $x^5{y}^7$
3. $x^7{y}^7$
4. $x^5{y}^5$

Q. Find $x$ if $3^{-x}=\frac{1}{3^2}.$

1. $-3$
2. $3$
3. $-2$
4. $2$

Q. What is the value of $a$ that satisfies the equation $2^5\times 4^5=2^a$?

1. 5
2. 10
3. 12
4. 15

Q.

Value of iota $502$

Q. Solve the following using laws of exponents and arrange them in ascending order.

1. ${10}^4÷{10}^2$
2. ${10}^3\times {10}^2$
3. ${10}^8÷{10}^2$
4. ${10}^3\times {10}^7$

Q. Evaluate:
$(5^{-1}\times 2^{-1})\times 6^{-1}$
[1 mark]

Q. If $(9{)}^{x+2}=240+9^x$, then $x=$

1. $0.2$
2. $0.1$
3. $0.4$
4. $0.5$

Q.

Express the following in the exponential form :

$2\times 2\times a\times a$

Q. If $(x+\frac{1}{x})=\frac{10}{3}$, then ${(x-\frac{1}{x})}^2$ is

1. ${\left(\frac{7}{3}\right)}^2$
2. ${\left(\frac{8}{3}\right)}^2$
3. ${\left(\frac{10}{3}\right)}^2$
4. ${\left(\frac{5}{3}\right)}^2$

Q. What will be the product of $p^2-3pq$ and $q^2+4pq$?

1. $pq(4p^2+3q^2+11pq)$
2. $pq(4p^2-3q^2-11pq)$
3. $pq(-4p^2+3q^2-11pq)$
4. $pq(4p^2-3q^2+11pq)$