Multiplying Terms with the Same Base

Q. Find the value of x, if $2^x\times 2^{10}=2^{-4x}$.

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

Q. $a^m\times a^n=$ _____

1. $a^{m+n}$
2. $a^{\frac{m}{n}}$
3. $a^{mn}$
4. $(a^m{)}^n$

Q. Find the value of $(-8{)}^{-2}\times (-8{)}^{-3}$

1. $(-8{)}^5$
2. $\frac{1}{(-8{)}^5}$
3. $(-8{)}^{-5}$
4. $\frac{1}{(8{)}^5}$

Q. If $(5{)}^{m+3}\times (5{)}^{-2}=(5{)}^5$, find the value of m.

1. m=5
2. m=2
3. m=4
4. m=3

Q. Find the value of x if $2^6\times 2^{2x}=2^{10}$

1. x=1
2. x=2
3. x=3
4. x=4

Q. Simplify $5^{10}\times 5^{30}\times 5^{40}$

1. $5^{-80}$
2. $5^{90}$
3. $5^{80}$
   
4. $5^{-90}$

Q.

Find the value of the following expression:

${\left({32}^{-2/5}\right)}^{1/2}$

Q. 4³ × 4⁴ =

1. 8⁷
2. 4⁷
3. 16¹²
4. 4¹²

Q. Evaluate $\frac{a^3\times a^5}{(a^3{)}^2}$.

1. $a^4$
   
2. $a^5$
   
3. $a^3$
   
4. $a^2$
   

Q. Find the value of $4^2\times 4^2$

1. 1
2. 256
3. $4^0$
4. $4^4$

Q.

Fill in the blanks with $<,>$ or $=$ sign: $2^3$ ______ $3^2$

Q. Simplify $5^2\times 5^3$

1. $5^6$
2. $5^5$
3. $5^1$
4. $5^4$

Q.

MULTIPLYING AND DIVIDING IN SCIENTIFIC NOTATION

Find the product or quotient. Write your answer in scientific notation.

$(1.2\times {10}^{-5})÷4$

Q. Simplify and express the following in exponential form:
$\left[{\left(5^2\right)}^3\right]÷5^7$

Q. Find the value of 'a', if $3^5\times 3^a=3^9$

1. a=3
2. a=-4
3. a=4
4. a=2

Q. Find the value of $2^{-5}\times 2^4$.

1. $2^9$
2. $2^{-3}$
3. $2^{-1}$
4. $2^{-20}$

Q. Simplify $m^5\times m^6$​​​​​​

1. $m^{30}$
2. $m^{11}$
3. $m^{-9}$
4. $m^9$

Q.

Choose the correct answer and fill in the blanks:

${\left({100}^5\right)}^0=\_\_\_\_\_\_.(100000/1)$

Q.

On multiplying terms with the same base, the exponents are ____.

1. multiplied

2. subtracted

3. added

4. divided

Q.

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

$2^5\times 5^5$

Q.

Write the following using positive exponents only :

$\frac{{\left(-3\right)}^0\times {\left(2^2\right)}^{-2}\times 9^2}{{\left(5^2\right)}^{-3}\times 3^2}$

Q.

Express in exponential form:

$\mathrm{b}\times \mathrm{b}\times \mathrm{b}\times \mathrm{a}\times \mathrm{a}$.

Q.

Using laws of exponents , simplify : ${\left(6a^2{b}^2\right)}^3+{\left(3a^2\right)}^4$

Q. Find the value of n, if

$(\frac{5}{3}{)}^{2n+1}\times (\frac{5}{3}{)}^5=(\frac{5}{3}{)}^{n+2}.$

1. $n=-4$
2. $n=0$
3. $n=4$
4. $n=1$

Q. Solve for $x$ in the equation $(-5{)}^{x+1}\times (-5{)}^5=(-5{)}^7$.

1. 6
2. 7
3. 2
4. 1

Q.

Evaluate $4^4\times 4^{-3}\times 4^2\times 4^{-5}$

1. 4

2. $\frac{1}{16}$

3. 16

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

Q.

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

$2^3$ and ${\left(3\right)}^2$ are _________ (same/different)

Q.

Simplify :

(v) $3^2\times {10}^4$

Q. Simplify, giving solution with positive index
$(-a^5)\left(a^2\right)$

Q.

How do you multiply ${\left(-5x^4{y}^2\right)}^3$.