Exponential Representation for Irrational Numbers

Q.

Express $\overline{1.27}$ in the form of $\frac{p}{q}$.

Q.

How do you simplify ${32}^{\frac{1}{5}}$ ?

Q.

Simplify:
$\frac{25\times t^{-4}}{5^{-3}\times 10\times t^{-8}}where,(t\ne 0)$

Q. Simplify:${64}^{-\frac{1}{3}}[{64}^{\frac{1}{3}}-{64}^{\frac{2}{3}}]$

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

Q. Question 19
The value of $\sqrt[4]{4(81{)}^{-2}}$ is

A) $\frac{1}{9}$
B) $\frac{1}{3}$
C) $9$
D) $\frac{1}{81}$

Q.

Simplify $\sqrt[4]{4\sqrt[3]{3x^2}}$ and express the result in the exponential form of x.

Q.

Simplify and express the result in power notation with positive exponent:

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

Q. 16√75÷5√12

Q. Evaluate:

Q.

Expand ${\left(\frac{7}{9}\right)}^3$?

1. 343/729

2. 729/343

3. 49/81

4. 81/49

Q.

Find the value of ${11}^2$

Q. If $p^{x–1}=qr,q^{y–1}=rp,r^z–1=pq,$ then the value of $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$ equals

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

Q.

Question 121

$\frac{16\times {10}^2\times 64}{2^4\times 4^2}$

Q.

What is ${\frac{121}{169}}^{\frac{-3}{2}}$?

1. 2197/1331

2. 13/11

3. 11/13

4. 1331/2197

Q.

Question 177(vi)

Find x.

$5^x+5^{x-1}=750$

Q.

If $\begin{array}{rcl}{\left[\frac{\left(1+i\right)}{\left(1-i\right)}\right]}^3-{\left[\frac{\left(1-i\right)}{\left(1+i\right)}\right]}^3& =& x+iy\end{array}$, then

1. $x=0,y=-2$

2. $x=-2,y=0$

3. $x=1,y=1$

4. $x=-1,y=1$

Q.

Third power of $\frac{1}{4}\times$ fourth power of 4 equals to ______.

1. $4^2$

2. $4^3$

3. $4$

4. $4^0$

Q.

Simplify $\frac{4}{{\left(216\right)}^{-2/3}}+\frac{1}{{\left(256\right)}^{-3/4}}+\frac{2}{{\left(243\right)}^{-1/5}}$

Q.

Simplify $({\sqrt{256})}^{\frac{-3}{4}}$

1. 8

2. 4

3. 1/8

4. 1/2

Q. ${\left(\frac{5^{-1}\times 7^2}{5^2\times 7^4}\right)}^{\frac{7}{2}}\times {\left(\frac{5^{-2}\times 7^3}{5^3\times 7^{-5}}\right)}^{\frac{-5}{2}}$

Q. Evaluate: $\frac{x^p}{x^p+x^q}+\frac{1}{x^{p-q}+1}.$

Q. Find the value of $x$
$5^{2x+1}÷25=125$

Q.

What is the absolute value of $\sqrt{2}$?

Q.

Which of the following is an irrational number?

i) $2\sqrt{3}$

ii) $0.143\overline{32}$

iii) $5.\overline{46}$

iv) $\sqrt{5}$

Q.

Simplify $-i^3$

Q. Simplify and express the result in power notation with positive exponent.
$(-4{)}^5÷(-4{)}^8$

Q. If$\frac{9^n\times 3^2\times {(3}^{-\frac{n}{2}}{)}^{-2}-{27}^n}{3^{3m}\times 2^3}=\frac{1}{27}$ Prove that m-n=1

Q. Evaluate ${\left(\frac{1}{5}\right)}^{2/3}\times {\left(\frac{1}{5}\right)}^{1/3}$

1. $\frac{1}{5}$
2. $\frac{1}{25}$
3. $25$
4. $5$

Q.

Write $\frac{345}{100}$in the point form.

Q. If $a^x=b^y=c^z$ and $b^2=ac,$ Prove that y=$\frac{2xz}{Z+x}$