Exponential Form through Prime Factorization

Q. Express 216 in exponential form.

1. $2^3\times 3^3$
2. $2^3\times 3^2$
3. $2^2\times 3^2$
4. $2^2\times 3^3$

Q.

Write $343$ in exponential form.

Q.

Question 78 (a)

Express each of the following numbers using exponential notations.
1024

Q.

If the LCM of $p,q$ is $r^2{t}^4{s}^2$, where $r,s,t$ are prime numbers and $p,q$ are the positive integers then the number of ordered pair $\left(p,q\right)$ is equal to:

1. $252$

2. $254$

3. $225$

4. $224$

Q. Express 250 as the product of exponents through prime factorization.

1. $5^3$
2. $2^1\times 5^2$
3. $2^1\times 5^3$
4. $2^1\times 5^4$

Q. We can represent 196 in exponential form as .

1. $2^3\times 7^2$
2. $2^2\times 7^2$
3. $2^2\times 7^3$
4. $2^2\times 7$

Q. Express 450 in exponential form.

1. $2\times 3\times 5$
2. $2\times 3^2\times 5$
3. $2\times 3^2\times 5^3$
4. $2\times 3^2\times 5^2$

Q. Find the value of a, b and c if $450=2^a\times 3^b\times 5^c$

1. $a=0,b=2,c=2$
2. $a=1,b=2,c=2$
3. $a=1,b=3,c=2$
4. $a=1,b=2,c=3$

Q. Find the value of:
$7^5$

Q. How to write a negative number in exponent form? Eg: -343

Q.

Find $(0.4p-0.5q{)}^2$. If p = 5 and q = 4, evaluate the value of the expression. [3 MARKS]

Q. Write the exponential form of $512\times 625$

1. $2^8\times 5^4$
2. $2^8\times 5^5$
3. $2^9\times 5^4$
4. $2^9\times 5^5$

Q. Express each of the following as product of powers of their prime factors:
$540$

Q.

Write the following in product form :

$\mathbf{7}{\mathit{p}}^{\mathbf{3}}{\mathit{q}}^{\mathbf{4}}{\mathit{r}}^{\mathbf{5}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{7}\mathbf{}\mathbf{\times }\mathbf{}\mathit{p}\mathbf{}\mathbf{\times }\mathbf{}\mathit{p}\mathbf{}\mathbf{\times }\mathbf{}\mathit{p}\mathbf{}\mathbf{\times }\mathbf{}\mathit{q}\mathbf{}\mathbf{\times }\mathbf{}\mathit{q}\mathbf{}\mathbf{\times }\mathbf{}\mathit{q}\mathbf{}\mathbf{\times }\mathbf{}\mathit{q}\mathbf{}\mathbf{\times }\mathbf{}\mathit{r}\mathbf{}\mathbf{\times }\mathbf{}\mathit{r}\mathbf{}\mathbf{\times }\mathbf{}\mathit{r}\mathbf{}\mathbf{\times }\mathbf{}\mathit{r}\mathbf{}\mathbf{\times }\mathbf{}\mathit{r}$

Q.

The quotient when p$q^2$+ 5pq+6p is divided by pq+2p is

1. q+3

2. q-3

3. q+2

4. pq+3p

Q.

One of the factors of the expression $(2x{)}^2+10x$ is $2x+3$.

1. True

2. False

Q.

Write the given expression in exponential form:

$2\times 2\times 2\times 3\times 3\times 3$

Q.

Write in the form of exponential notation.

$3\times 3\times 3\times 3\times 3\times 3\times 3$

Q. Find the value of 'p' and 'q' if 2100=$2^2\times p\times q\times 7$

1. $p=3,q=5^3$
2. $p=3,q=5$
3. $p=3,q=5^2$
4. $p=5,q=3^2$

Q.

Write the given expression in exponential form:

$6\times 6\times 8\times 8\times 8$

Q. Express each of the following numbers using exponential notation:
$729$

Q.

Express 2352 in exponential form.

1. $2^4\times 7^2$

2. $2^2\times 3^1\times 7^2$

3. $2^4\times 3^1\times 7^3$

4. $2^4\times 3^1\times 7^2$

Q. Express each of the following numbers using exponential notation:
$343$

Q. Express each of the following as product of powers of their prime factors:
$405$