Rational Exponents

Q.

The standard form for $234000000$ is

1. $2.34\times {10}^8$

2. $0.234\times {10}^9$

3. $2.34\times {10}^{-8}$

4. $0.234\times {10}^{-9}$

Q.

The cost of putting a square fence around a square field at $27Rspermeter$ is $5292Rs.$ The length of each side of the field is :

1. $98m$

2. $122.5m$

3. $196m$

4. $49m$

Q. Find the value of $(\frac{729}{512}{)}^{-\frac{2}{3}}$.

1. $\frac{81}{64}$
   
2. $\frac{64}{81}$
   
3. $\frac{9}{8}$
   
4. $\frac{8}{9}$
   

Q. If ${4096}^{\frac{x}{4}}=512$, find the value of $x$.

1. $x=8$
2. $x=2$
3. $x=3$
4. $x=4$

Q. What will be the value of $(8{)}^{\left(3^{-1}\right)}$ ?

1. 24
2. $\frac{8}{3}$
3. 2
4. $\frac{1}{2}$

Q. Find the value of $(243{)}^{-\frac{4}{5}}$.

1. $81$
2. $\frac{1}{81}$
   
3. $27$
4. $\frac{1}{27}$
   

Q.

State whether the given statement is True or False: ${(-\frac{3}{5})}^{100}=\left(\frac{-3^{100}}{-5^{100}}\right)$

1. True
2. False

Q. Andie is trying to calculate cost of building a fence around a square field. The area of the square field is 40, 000 $m^2$ and the fencing he wants to put around the perimeter costs $ 4.5 per meter. What would be the total cost of fencing the square field ?

1. 3200 $
2. 3400 $
3. 3600 $
4. 3800 $

Q. 109875654 is a large number. It can be represented using exponents.

1. True
2. False

Q. If ${243}^{\frac{2}{y}}=9$, find the value of $y(y\ne 0)$.

1. $y=4$
2. $y=5$
3. $y=3$
4. $y=9$

Q. Simplify $\sqrt[3]{327P^{27}}$

1. $27P^3$
2. $3P^{27}$
3. $3P^9$
4. $3P^3$

Q.

Which one is greater in each of the following?

(ii) $5^3$ or $3^5$

Q. ${81}^{\frac{1}{4}}\times 9^{\frac{3}{2}}\times {27}^{\frac{-4}{3}}$ is equal to ______.

Q. The value of $(\frac{1}{216}{)}^{-\frac{1}{3}}$ is
.

Q. What is the simplest form of the expression $(M^2{)}^{\frac{5}{6}}\times M^{\frac{1}{3}}$ ?

1. $M^{\frac{2}{3}}$
2. $M^{\frac{11}{6}}$
3. $M^2$
4. None of the above

Q. Simplify the following expression such that the result has positive exponents: $\left(25M^2{N}^{-4}{)}^{1/2}\right(M^3{N}^{1/2}{)}^2$.

1. $5M^7/N$
2. $25M^5/N$
3. $5M^5/N$
4. $5M^6/N$