Powers with Negative Exponents

Q.

By what number should $(-6{)}^{-1}$ be multiplied so that the product becomes $9^{-1}$ ?

Q.

Write the cubes of number $1$ to $25$.

Q.

If $z=1+i$, then the multiplicative inverse of $z^2$ is

1. $2i$

2. $1-i$

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

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

Q.

By what number should $5^{-1}$ be multiplied so that the product may be equal to $(-7{)}^{-1}$ ?

Q.

Multiplicative inverse of ${10}^{-100}$ is:

1. ${10}^{100}$

2. ${10}^{-100}$

3. 10

4. 100

Q.

By what number should ${\left(\frac{1}{2}\right)}^{-1}$ be multiplied so that the product many be equal to ${\left(\frac{-4}{7}\right)}^{-1}?$

Q.

Question 92

Express $3^{-5}\times 3^{-4}$ as a power of 3 with positive exponent.

Q.

Express each of the following as a rational number of the form $\frac{p}{q}$, where p and q are integers and $q\ne 0:\left(i\right)2^{-3}\left(ii\right)(-4{)}^{-2}(iii\left)\frac{1}{3^{-2}}\right(iv\left){\left(\frac{1}{2}\right)}^{-5}\right(iv){\left(\frac{2}{3}\right)}^{-2}$

Q.

Simplify and express each of the following in exponential form: $\frac{(3\times 7^2\times {11}^8)}{(21\times {11}^3)}$.

Q.

The value of${512}^{\frac{-2}{9}}$ is

Q.

The reciprocal of ${\left(\frac{2}{5}\right)}^{-1}$is:

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

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

3. $\frac{-5}{2}$

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

Q.

Simplify the following: $(81{)}^{-\frac{1}{4}}$

Q.

$\{{\left(\frac{1}{3}\right)}^{-3}-{\left(\frac{1}{2}\right)}^{-3}\}÷{\left(\frac{1}{4}\right)}^{-3}=?$

$\left(a\right)\frac{19}{64}$

$\left(b\right)\frac{27}{16}$

$\left(c\right)\frac{64}{19}$

$\left(d\right)\frac{16}{25}$

Q.

Evaluate:

$\left(i\right)5^{-2}\left(ii\right)(-3{)}^{-2}(iii\left){\left(\frac{1}{3}\right)}^{-4}\right(iv){\left(\frac{-1}{2}\right)}^{-1}$

Q.

The value of $(-2{)}^{-5}$ is

(a)-32

$\left(b\right)\frac{-1}{32}$

(c)32

$\left(d\right)\frac{1}{32}$

Q.

$\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{3.4}-\frac{1}{4.5}+...is$

1. $2\log 2-1$

2. $3\log 2$

3. $4\log 2–1$

4. $Noneofthese$

Q.

Evaluate $\{{\left(\frac{1}{3}\right)}^{-3}-{\left(\frac{1}{2}\right)}^{-3}\}÷{\left(\frac{1}{4}\right)}^{-3}$

Q.

${(-\frac{5}{7})}^{-5}$ is equal to :

1. ${\left(\frac{5}{7}\right)}^{-5}$

2. ${\left(\frac{7}{5}\right)}^{-5}$

3. ${(-\frac{7}{5})}^{-5}$

4. ${(-\frac{7}{5})}^5$

Q.

${\left(\frac{-5}{7}\right)}^{-5}=\_\_$

1. ${\left(\frac{5}{7}\right)}^{-5}$

2. ${\left(\frac{5}{7}\right)}^5$

3. ${\left(\frac{7}{5}\right)}^5$

4. ${\left(\frac{-7}{5}\right)}^5$

Q.

The value of $(\frac{2}{5}{)}^{-3}$ is

$\left(a\right)-\frac{8}{125}$

$\left(b\right)\frac{25}{4}$

$\left(c\right)\frac{125}{8}$

$-\frac{2}{5}$

Q.

Question 3

In the following question, out of the four options, only one is correct. Write the correct answer:

$3^{-2}$ can be written as:
(a) $3^2$
(b) $\frac{1}{3^2}$
(c) $\frac{1}{3^{-2}}$
(d) $-\frac{2}{2}$

Q.

Find the multiplicative inverse of ${10}^{-10}$.

1. 10000000

2. 10000000000

3. 0.0000000001

4. 0.000000001

Q. $4^{2x-1}-{16}^{x-1}=348$ find x

Q.

The multiplicative inverse of ${\left(\frac{-5}{9}\right)}^{-99}$is?

1. ${\left(\frac{-5}{9}\right)}^{99}$

2. ${\left(\frac{5}{9}\right)}^{99}$

3. ${\left(\frac{9}{-5}\right)}^{99}$

4. ${\left(\frac{9}{5}\right)}^{99}$

Q.

${\left(\frac{-7}{5}\right)}^{-1}=\_\_$

1. $\frac{5}{7}$

2. $\frac{-5}{7}$

3. $\frac{7}{5}$

4. $\frac{-7}{5}$

Q.

Find the value of:

$\left(1\right)(2^0+3^{-1})\times 3^2$

$\left(ii\right)(2^{-1}\times 3^{-1})÷2^{-3}$

$\left(iii\right){\left(\frac{1}{2}\right)}^{-2}+{\left(\frac{1}{3}\right)}^{-2}+{\left(\frac{1}{4}\right)}^{-2}$

Q.

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

$6^{15}÷6^{10}$

Q.

Question 35
$(213\times 657{)}^{-1}=(213{)}^{-1}\times$ ___.

Q.

Express the following in exponential form: $6\times 6\times 6\times 6$

Q. -1 raised to any integral power would give the value of -1.

1. True
2. False