Fractional Exponent

Q. Question 11
Find the values of a and b in each of the following
$\left(i\right)\frac{5+2\sqrt{3}}{7+4\sqrt{3}}=a-6\sqrt{3}$
$\left(ii\right)\frac{3-\sqrt{5}}{3+2\sqrt{5}}=a\sqrt{5}-\frac{19}{11}$
$\left(iii\right)\frac{\sqrt{2}+\sqrt{3}}{3\sqrt{2}-2\sqrt{3}}=2-b\sqrt{6}$
$\left(iv\right)\frac{7+\sqrt{5}}{7-\sqrt{5}}-\frac{7-\sqrt{5}}{7+\sqrt{5}}=a+\frac{7}{11}\sqrt{5}b$

Q.

Question 3 (iv)
Simplify:

$7^{\frac{1}{2}}{.8}^{\frac{1}{2}}$

Q.

Simplify : $\frac{1}{\sqrt{2}}$

Q.

$\int \frac{\left(4^{x+1}-7^{x-1}\right)}{{28}^x}=$

1. $\left(\frac{1}{7{\log }_{e}4}\right)4^{-x}-\left(\frac{4}{{\log }_{e}7}\right)7^{-x}+C$

2. $\left(\frac{1}{7{\log }_{e}4}\right)4^{-x}+\left(\frac{4}{{\log }_{e}7}\right)7^{-x}+C$

3. $\left(\frac{1}{{\log }_{e}7}\right)-\left(\frac{7^{-x}}{{\log }_{e}4}\right)+C$

4. $\left(\frac{4^{-x}}{{\log }_{e}4}\right)-\left(\frac{7^{-x}}{{\log }_{e}7}\right)+C$

5. $\left(\frac{1}{28}\right){\log }_e{4}^{-x}+\left(\frac{1}{7}\right){\log }_e{7}^{-x}+C$

Q. The greatest number among $\sqrt[3]{39}$, $\sqrt[4]{411}$, $\sqrt[6]{617}$, $\sqrt[8]{881}$.

1. $\sqrt[3]{39}$.
2. $\sqrt[4]{411}$
3. $\sqrt[6]{617}$
4. $\sqrt[8]{881}$

Q.

Rationalize the denominator of the following:

$\frac{1}{(\sqrt{7}-\sqrt{6})}$

Q.

Convert $7.6c{m}^{3}to{m}^3$.

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

1. ${10}^{-1}$
2. ${10}^{-2}$
3. ${10}^{-3}$
4. ${10}^{-4}$

Q. If $x=\sqrt{13}+2\sqrt{3}$, find the value of $x-\frac{1}{x}$.

Q.

Evaluate:- $(\frac{27}{125}{)}^{\frac{2}{3}}\times (\frac{9}{25}{)}^{\frac{-3}{2}}$

1. $\frac{3}{5}$

2. $\frac{5}{4}$

3. $\frac{5}{3}$

4. $\frac{4}{3}$

Q.

Express $(3\times {10}^2)+(2\times {10}^1)+(9\times {10}^0)+(2\times {10}^{-1})+(5\times {10}^{-2})$ as a numeral.

1. 32.925

2. 3292.5

3. 329.25

4. 3.2925

Q. Question 12
The number obtained on rationalising the denominator of $\frac{1}{\sqrt{7}-2}$ is

A) $\frac{\sqrt{7}+2}{3}$
B) $\frac{\sqrt{7}-2}{3}$
C) $\frac{\sqrt{7}+2}{5}$
D) $\frac{\sqrt{7}+2}{45}$

Q.

If \(\sqrt{2}~=~1.4\), then the value of \(\sqrt{98}\) is ___

Q. Find the value of $\frac{1}{\sqrt{10}}$. If $\sqrt{10}$ =3.162

Q. Evaluate: $(6.25{)}^{\frac{3}{2}}$

1. $15.625$
2. $18.236$
3. $20.147$
4. $12.5$

Q.

Fill in the boxes.

${\left[5^{\square }\right]}^5÷5^{-10}=1$

Q. Simplify $\frac{x^{a+b}\times x^{b+c}\times x^{c+a}}{(x^a\times x^b\times x^c)}$

Q.

$\left(\right({{{\left(625\right)}^{-\frac{1}{2}})}^{\frac{-1}{4}})}^2$

Q. Evaluate: $(6^2+8^2{)}^{\frac{1}{2}}$

Q.

Question 180(ii)

Simplify

${[{\left(\frac{4}{3}\right)}^{-2}-{\left(\frac{3}{4}\right)}^2]}^{-2}$

Q. Simplify:
i) ${64}^{\frac{1}{3}}$
ii) ${81}^{\frac{3}{4}}$

Q.

Simplify the expression. Write your answer as a power.

${\left(5^4\right)}^2$.

Q.

Evaluate

$-8\frac{1}{3}+2\frac{3}{7}$

Q. Solve:
$\frac{8^{-1}\times 5^3}{2^{-4}}$

Q. Simplify:
$[{\left(\frac{1}{3}\right)}^{-3}-{\left(\frac{1}{2}\right)}^{-3}÷{\left(\frac{1}{5}\right)}^{-2}]$

Q.

Solve :$(7x-9y{)}^3$

Q.

Prove that:

$\frac{2^n+2^{n-1}}{2^{n+1}-2^n}=\frac{3}{2}$

Q. Evaluate: $(0.04{)}^{{}^{\frac{3}{2}}}$

1. $0.08$
2. $0.001$
3. $0.008$
4. $0.01$

Q. Evaluate $\frac{3\times {27}^{n-1}+9\times 3^{3n-1}}{8\times 3^{3n}-5\times {27}^n}$

Q. Rationalize the denominator of the following
$\left(i\right)\frac{2}{3\sqrt{3}}\left(ii\right)\frac{\sqrt{40}}{\sqrt{3}}$

[ 3 marks ]