Powers with Negative Exponents

Q.

Find the multiplicative inverse of 10${}^{-5}$.

1. $0.00001$

2. $-50$

3. $-100000$

4. $100000$

Q.

Prove that $9^{3/2}-3\times 5^0-{\left(\frac{1}{81}\right)}^{-1/2}=15$.

Q. $(-x{)}^{-y}$ is equal to

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

Q.

For a non-zero rational number $x$, $x^8÷x^2$ is equal to

(a) $x^4$
(b) $x^6$
(c) $x^{10}$
(d) $x^{16}$

Q.

Simplify: $\frac{\left(2^5\times 5^2\times t^8\right)}{\left({10}^3\times t^4\right)}$

Q. Simplify and write the expression in exponential form: $4^3$ x $4^{-2}$ x ${16}^2$

Q. (a) Give the additive inverse of:
$\frac{3}{14},\frac{-5}{19}$

(b) Give the multiplicative inverse of $\frac{-3}{4}$

[2 MARKS]

Q. Which of the following is the multiplicative inverse of ${(-\frac{5}{2})}^{-3}$?

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

Q.

Arrange the following in ascending order.

$\frac{2}{9},\frac{6}{7},\frac{1}{10},\frac{3}{5},\frac{7}{11}$

Q. While expressing $\frac{1}{8}$ in exponential form, the base is and the exponent is .

1. 2
2. -2
3. 3
4. -3

Q. Evalute:
$2^3÷2^8$

Q. What is the value of $7^{-2}$?

1. $\frac{-1}{49}$
2. $\frac{1}{49}$
3. $\frac{1}{14}$
4. 14

Q. The simplified form of $(256{)}^{0.16}\times (256{)}^{0.09}$ is:

1. $4$
2. $64$
3. $256.25$
4. $16$

Q. If $a=-1$ and $b=2,$ then $\frac{a^b\times b^a}{b-2a}$ = ___.

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

Q. $\frac{4.2\times 4.2-1.9\times 1.9}{2.3\times 6.1}$ is equal to:

1. $22$
2. $20$
3. $1.0$
4. $0.5$

Q. The mass of an electron is approximately equal to $9\times {10}^{-31}$ kg. If the total mass of an atom is $18\times {10}^{-25}$ kg, find the ratio of the mass of an electron to the total mass of an atom.

1. $\frac{1}{2\times {10}^6}$
2. $2\times {10}^6$
3. $\frac{1}{2\times {10}^5}$
4. $2\times {10}^5$

Q. If $3^x=\frac{1}{81}$, then find the value of $x$.

Q. Match column I with column II and select the correct answer by using the given codes.
$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{(A)}& {\left(\frac{4^{10}}{4^{15}}\right)}^{1/5}& \text{(P)}& \frac{1}{16}\\ \text{(B)}& {\left(\frac{7^{20}}{7^{30}}\right)}^{1/5}& \text{(Q)}& \frac{1}{49}\\ \text{(C)}& {\left(\frac{{49}^{49}}{{49}^{51}}\right)}^{1/4}& \text{(R)}& \frac{1}{4}\\ \text{(D)}& {\left(\frac{{16}^{27}}{{16}^{31}}\right)}^{1/4}& \text{(S)}& \frac{1}{7}\end{array}$

1. $A\to R;B\to S;C\to Q;D\to P$
2. $A\to R;B\to S;C\to P;D\to Q$
3. $A\to R;B\to Q;C\to S;D\to P$
4. $A\to R;B\to P;C\to Q;D\to S$

Q.

Simplify and write the expression in exponential form: $4^3$ x $4^{-2}$ x ${16}^2$

1. $4^3$

2. $4^4$

3. $4^5$

4. $4^6$

Q. Simplify the following using law of exponents.
$\frac{9^7}{9^{15}}$

1. $9^{-8}$
2. $\frac{1}{9^8}$
3. $9^8$
4. $9^{1/8}$

Q. Simplify $(x^{-1}+y^{-1})$.

1. $\frac{x}{x+y}$
2. $\frac{x+y}{xy}$
   
3. $\frac{x+y}{x+y}$
4. 
   $\frac{x+y}{-xy}$

Q.

Simplify
$\left\{\frac{1}{6^{(-2)}}-\frac{1}{3^{(-3)}}\right\}÷\frac{1}{5^{(-2)}}$

1. $(\frac{3}{5}{)}^2$

2. $(\frac{9}{25}{)}^2$

3. $(\frac{5}{3}{)}^2$

4. $(\frac{25}{9}{)}^2$

Q.

What is the value of ${\left(\right(2{)}^{-1})}^{-2}$?.Give your answer in numerals

__

Q.

Express "1 divided by (9x9x9)" in exponential form.

1. 729

2. 9^-3

3. 9^3

4. 1/9^-3

Q.

Find the value of $7^{-3}$.

1. $\frac{1}{343}$

2. $\frac{1}{49}$

3. $343$

4. $\frac{1}{21}$

Q.

Find the value of $({\left(\frac{3}{2}{)}^{-1}\right)}^{-2}.$

1. $\frac{4}{9}$

2. $\frac{-9}{4}$

3. $\frac{-4}{9}$

4. $\frac{9}{4}$

Q.

$(\frac{2}{5}{)}^2=-(\frac{2}{5}{)}^2$

1. False

2. True

Q. Which among the following would be equal to $3^{-5}\times 3^{-2}$?

1. $3^7$
2. $3^{-10}$
3. $3^{10}$
4. $3^{-7}$

Q.

Find the value of $7^{-3}$.

1. $343$

2. $\frac{1}{343}$

3. $49$

4. $\frac{1}{49}$

Q. Divide
$(5p^2-25p+20)÷(p-1)$