Normal Form to Standard Form

Q.

Find the value of ‘m‘ if $(-2{)}^2\times (-5{)}^3=50m$

1. -10

2. 10

3. -100

4. 100

Q.

Solve: $3^{x-1}\times 5^{2y-3}=225$

Q. Question 21
Which of the following is equal to x?

A) $x^{\frac{12}{7}}-x^{\frac{5}{7}}$
B) $\sqrt[12]{12(x^4{)}^{\frac{1}{3}}}$
C) ${\left(\sqrt{x^3}\right)}^{\frac{2}{3}}$
D) $x^{\frac{12}{7}}\times x^{\frac{7}{12}}$

Q.

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

Q.

If $2160=2^a.3^b.5^c$, find a, b and c. Hence calculate the value of $3^a\times 2^{-b}\times 5^{-c}$

Q.

Find $x$, if:

(i) $4^{2x}=\frac{1}{32}$

(ii) $\sqrt{2^{x+3}}=16$

(iii) ${\left(\sqrt{\frac{3}{5}}\right)}^{x+1}=\frac{125}{27}$

(iv) ${\left(\sqrt[3]{3\frac{2}{3}}\right)}^{x-1}=\frac{27}{8}$

Q.

Question 132

The planet Uranus is approximately 2, 896, 819, 200, 000 metres away from the Sun. What is this distance in standard form?

Q.

Question 51

Fill in the blanks to make the statement true.

$[12\times (-7\left)\right]\times 5=$ ___ $\times$ $\left[\right(-7)\times$___ $]$

Q. Prove that:
${\left(\frac{1}{4}\right)}^{-2}-3\times 8^{\frac{2}{3}}\times 4^0+{\left(\frac{9}{16}\right)}^{-\frac{1}{2}}=\frac{16}{3}$

Q.

Solve

$3^{x^2}:3^x=9:1$.

1. $x=1,-1$

2. $x=2,-1$

3. $x=2,-2$

4. $x=0,-1$

Q. Express 12470000000000 in the standard form.

1. $124.7\times {10}^{10}$
2. $12.47\times {10}^{13}$
3. $1.247\times {10}^{13}$
4. $12.47\times {10}^{-13}$

Q.

Q. Solve:
$28-31x-5x^2=0$

Q. Expand ${(\frac{1}{x}+\frac{y}{3})}^3$

Q.

Fill in the boxes.

$\frac{{\left(3^2\right)}^3\times {\left(5^2\right)}^{-3}}{5^{-6}}={\left[3^{\square }\right]}^2$

Q. Solve :
$\frac{xdx+ydy}{\sqrt{x^2+y^2}}=\frac{xdy-ydx}{x^2}$

Q.

Solve for $x$

$3^{4x+1}={27}^{x+1}$

1. -2

2. 1

3. 2

4. -1

Q.

Q. Solve : $(x^4-{3x}^3-8)÷(x-4)$

Q. Solve $(x+y{)}^3-(x-y{)}^3$.

Q.

$\text{If}x+\frac{1}{x}=2,\text{find the value of}{x}^{64}+\frac{1}{x^{64}}$

1. 32

2. 16

3. 8

4. 2

Q. Solve :

Q.

Solve for y if
$\frac{{\left(\frac{1}{9}\right)}^{2y-1}(.0081{)}^{\frac{1}{3}}}{\sqrt{243}}={\left(\frac{1}{3}\right)}^{2y-5}\sqrt[3]{3\frac{{27}^{y-1}}{10000}}$

1. $\frac{-19}{8}$

2. $19\times 8$

3. $\frac{-19}{18}$

4. $\frac{18}{9}$

Q. If $15625=(x{)}^2=5^{\left(y\right)}$ . Find the value of $x$ and $y$.

Q. Solve:

Q.

If $x=3$ and $y=-2$ then the value of $x^x+y^{-y}$ is ___

Q. Express 0.0000987 in standard form.

1. $9.87\times {10}^5$
2. $9.87\times {10}^{-5}$
3. $98.7\times {10}^6$
4. $98.7\times {10}^{-6}$

Q.

If $10800=2^a\times 3^b\times 5^c$ then find the value of a, b and c.

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

2. $a=3,b=3,c=2$

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

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

Q. Solve $16+8x-x^6-8x^3-2x^4+x^2$ by $x+4-x^3$

Q.

Solve for $x$

$2^{3x}=8^{3x+1}$

1. -2

2. 2

3. $\frac{-1}{2}$

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