Power of a Power

Q.

Find the value of ${\left(16\right)}^{\frac{3}{4}}$

Q.

Prove that ${\left(\frac{x^a}{x^b}\right)}^{1/ab}·{\left(\frac{x^b}{x^c}\right)}^{1/bc}·{\left(\frac{x^c}{x^a}\right)}^{1/ca}=1$

Q.

If ${27}^x=\frac{9}{3^x}$, find $x$.

Q.

What is $i^3$?

Q.

If $\sqrt{0.04\times 0.4\times a}=0.4\times 0.04\times \sqrt{b}$, the value of $\frac{b}{a}$ is

1. 0.016

2. $\frac{125}{2}$

3. 0.064

4. 0.16

Q.

Find the product: $\left(\frac{2}{3}xy\right)\times \left(-\frac{9}{10}{x}^2{y}^2\right)$

Q.

Question 22

Which power of 8 is equal to $2^6$?
(a) 3
(b) 2
(c) 1
(d) 4

Q.

Find the product: $a^2\times \left(2a^{22}\right)\times \left(4a^{26}\right)$

Q.

Question 85 (e)

Evaluate
${\left(\frac{6\times 10}{2^2\times 5^3}\right)}^2\times \frac{25}{27}$

Q.

If $\sqrt{1369}+\sqrt{0.0615+x}=37.25$, find the value of $x$?

1. ${10}^{-1}$

2. ${10}^{-2}$

3. $10$

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

Q.

${1400}^n$ is NOT divisible by which of the following, if n is a natural number:

1. 100

2. 175

3. 56

4. 210

Q. If $2^{2x-1}=\frac{1}{8^{x-3}}$, then find the value of '$x$'.

1. $3$
2. $1$
3. $4$
4. $2$

Q.

The value of ${}^{50}C_4+\sum _{r=1}^6\left({}^{56-r}C_3\right)$ is

1. ${}^{56}C_4$

2. ${}^{56}C_3$

3. ${}^{55}C_3$

4. ${}^{55}C_4$

Q.

Using laws of exponents, simplify and write the answer in exponential form:

$(2^{20}÷2^{15})\times 2^3$

Q.

$a^m\times b^m=(ab{)}^m$

1. True

2. False

Q. The value of $(243{)}^{-\frac{2}{5}}$ is _______.

1. $9$
2. $\frac{1}{9}$
3. $\frac{1}{3}$
4. $0$

Q.

What is $3$ to the power of $-1$?

Q.

The value of $2^{\frac{1}{4}}.4^{\frac{1}{8}}.8^{\frac{1}{16}}........\infty$ is

1. $1$

2. $2$

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

4. $4$

Q.

$a^m$ $\times$ $a^n$ = $a^{mn}$

1. True

2. False

Q. Question 1(viii)
Using laws of exponents, simplify and write the answer in exponential form:
(viii) $(3^4{)}^3$

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

Q.

For a complex number$z$, let $Re\left(z\right)$ denote the real part of $z$. Let $S$ be the set of all complex numbers $z$ satisfying$z^4-|z{|}^4=4i{z}^2$, where$i=\sqrt{(-1)}$. Then the minimum possible value of$|z_1-z_2{|}^2$, where$z_1,z_2\in S$with$Re\left(z_1\right)>0$ and$Re\left(z_2\right)<0$, is _____

Q. If '$x$' be any non-zero integer, then $x^0$ is equal to:

1. $0$
2. $1$
3. $-1$
4. Not defined

Q.

Question 14

Which of the following is not equal to ${\left(\frac{-5}{4}\right)}^4$?
(a) $\frac{(-5{)}^4}{4^4}$
(b) $\frac{5^4}{(-4{)}^4}$
(c) $-\frac{5^4}{4^4}$
(d) $(-\frac{5}{4})\times (-\frac{5}{4})\times (-\frac{5}{4})\times (-\frac{5}{4})$

Q. If $\frac{1872}{\sqrt{x}}=234$, then x is equal to

1. 8
2. 64
3. 256
4. 4

Q. Express $343\times 243$ in exponential form:

1. $x^{m-n}$
2. $\sqrt[n]{n{x}^m}$
3. $\sqrt[m]{m{x}^n}$
4. $m.x^{1/n}$

Q. Express 6561 as a power of a prime number.

1. 36

2. 94

3. 39
4. 38

Q.

Subtract $4pq-5q^2-3p^2$ from $5p^2+3q^2-pq$

Q. Question 1 (v)
Express each number as the product of its prime factors:
v) 7429

Q. How do you simplify ${\left(x^3\right)}^2$?