Product Law of Exponent

Q. While expressing $\frac{1}{8}$ in exponential form, the base is and the exponent is .

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

Q.

What is $2$ raised to the power $12$?

Q.

What is$10$ to the power of $7$?

Q.

${\left(\frac{3}{4}\right)}^5÷{\left(\frac{5}{3}\right)}^5$ is equal to:

1. ${\left(\frac{3}{4}÷\frac{5}{3}\right)}^5$

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

3. ${\left(\frac{3}{4}÷\frac{5}{3}\right)}^0$

4. ${\left(\frac{3}{4}÷\frac{5}{3}\right)}^{10}$

Q.

What is $2$ to the power of $50$?

Q. In $8^2$, is the base and is the exponent.

1. 8
2. 2
3. 64
4. 10

Q.

$3^4$ is greater than $4^3.$

1. True

2. False

Q.

Simplify and write the expression in exponential form: $4^3$ x $4^{-2}$ x ${16}^2$

1. 4⁶

2. 4³

3. 4⁴

4. 4⁵

Q. Match the following power with their corresponding power.

1. $729$
2. $3125$
3. $100$
4. $\frac{1}{4}$

Q.

The exponent of 'c' after simplifying $\left(3ab{)}^2\right(-5a^{2}b{c}^4{)}^2$ is

1. 4

2. 8

3. 12

4. 16

Q.

Evaluate $213\times 187$ using suitable identity

Q.

Simplify:
${(a-b)}^2+4ab$

1. +

2. 

3. -

4. - + 4ab

Q.

What is $2$ to the ${10}^{th}$ power?

Q. If ${}^n{P}_r=3024$, then $(n,r)=$

1. $(8,4)$
2. $(8,3)$
3. $(9,3)$
4. $(9,4)$

Q. The value of $\frac{6^{12}\times (35{)}^{28}\times (15{)}^{16}}{(14{)}^{12}\times (21{)}^{11}\times 5^{28}}$ is _____ .

1. $2^7\times 3^{17}\times 7^5$
2. $3^{17}\times 5^{16}\times 7^5$
3. $2^5\times 5^{16}\times 7^{12}$
4. $2^6\times 3^{16}\times 5^{12}$

Q.

$(x+y)(x-y)(x^2+y^2)$ is

1. x³ + y³

2. ( - )

3. ( + )

4. x⁴ - y⁴

Q.

Which one of the following is equivalent to $(2^x{)}^2$?

1. $2^{2x}$

2. $2^{2+x}$

3. $2^{2-x}$

4. $4^{2x}$

Q.

If $(2{)}^{m+1}\times 2^5=4^{-2}$, the value of $m$ is

1. -4

2. -6

3. -8

4. -10

Q.

Using laws of exponents, simplify and write the answer in exponential form:

(iii) $5^3\times 5^7\times 5^{12}$

Q.

Simplify
$(a^2+b^2)\times ({-a}^2+b^2)=?$

1. - +

2. -

3. -

4. +

Q.

$a\times$ $a^{-1}$ = 1

1. True

2. False

Q. ${90}^3$ is equal to

1. $729000$
2. $81000$
3. $27000$
4. $90000$

Q.

Using laws of exponents , simplify and write the answer in exponential form:

${\left(-3\right)}^4\times {\left(-3\right)}^5\times {\left(-3\right)}^2$

Q.

$(\frac{2}{5}{)}^2$ = $-(\frac{2}{5}{)}^2$

1. True

2. False

Q. Simplify and write in exponential form:
$3^3\times 3^{-2}\times {27}^2$

1. $3^6$

2. $3^7$

3. $3^3$

4. $3^5$

Q. Sort the following numbers in increasing order of their power of '4' from top to bottom.

1. $(4^{-3}{)}^2$
2. $4^3\times 4^2$
3. $2^2\times 8^2$
4. $(4^2{)}^{-2}$

Q.

Choose the correct word/answer and fill in the blanks :

$\frac{2^4}{5^4}=\_\_\_\_\_\_\_\left[{\left(\frac{2}{5}\right)}^4/{\left(\frac{2}{5}\right)}^{4-4}\right]$

Q.

Using laws of exponents , simplify and write the answer in exponential form:

${\left(4^3\right)}^4÷{\left(4^2\right)}^6$

Q.

The multiplicative inverse of $a^m$ is ___ .

1. 10000000

2. 0.000000001

3. 0.0000000001

4. 10000000000

Q. Simplify, $(\frac{1}{3}{)}^2\times 3^{-2}$

1. $\frac{1}{81}$
2. $\frac{1}{27}$
3. $27$
4. $81$