Free Printable Laws of indices

1.

$a^m\times a^n=$

a)

$a^m+a^n$

b)

$a^{m+n}$

c)

$a^{2mn}$

2.

$a^m\div a^n=$

a)

$a^{m-n}$

b)

$a^{m\div n}$

c)

$m\div n$

3.

$a^m\times b^m=$

a)

$\left(ab\right)^{2m}$

b)

$\left(ab\right)^{m^2}$

c)

$\left(ab\right)^m$

4.

$7^2\times7^3=$

a)

$7^5$

b)

$7^6$

c)

$14\times21$

d)

$49^{2\times3}$

5.

$\left(2^4\right)^3=$

a)

$8^3$

b)

$2^7$

c)

$2^{12}$

d)

$8^{12}$

6.

$3^3\times5^3=$

a)

$15^6$

b)

$15^3$

c)

$9\times15$

d)

$\left(3\times5\right)^9$

7.

Given that $5^x=u$ , what is $5^{2x}$ ?

a)

$2u$

b)

$u^2$

c)

$2u^2$

d)

$5u$

8.

If $x^{\frac{3}{2}}=4$ then

a)

$x=\frac{3}{2}\times4$

b)

$x=\frac{2}{3}\times4$

c)

$x=4^{\frac{3}{2}}$

d)

$x=4^{\frac{2}{3}}$

9.

Which of the following is TRUE?

a)

$7^{10}=\left(7^{20}\right)^{\frac{1}{2}}$

b)

$7^{10}=7^2+7^8$

c)

$7^{10}=7^{12}\div7^2$

d)

$7^{10}=7^2\times7^5$

10.

Simplify $3x^3\times6x^8$

a)

$18x^{11}$

b)

$18x^{24}$

c)

$9x^{11}$

d)

$9x^{24}$

11.

Solve $4^{a-1}=8^{a+3}$ .

a)

$a=-11$

b)

$a=-4$

c)

$a=4$

d)

$a=11$

12.

Solve $3^{a-2}\times27^a=\frac{1}{81}$ .

a)

$a=-2$

b)

$a=\frac{1}{2}$

c)

$a=2$

d)

$a=-\frac{1}{2}$

13.

Solve $2\div4^{a-1}=16^{2a}$ .

a)

$a=\frac{3}{10}$

b)

$a=\frac{10}{3}$

c)

$a=-\frac{10}{3}$

d)

$a=-\frac{3}{10}$

14.

Solve $32^{4x}=4^{8x+6}$ .

a)

$x=3$

b)

$x=-3$

c)

$x=-\frac{1}{3}$

d)

$x=\frac{1}{3}$

15.

Solve $9\left(3^{x-1}\right)=27^x$ .

a)

$x=-2$

b)

$x=2$

c)

$x=-\frac{1}{2}$

d)

$x=\frac{1}{2}$

16.

Solve $2^{\left(x+1\right)}\times4^{\left(2x-3\right)}=16^{\left(3x-2\right)}$

a)

$\frac{7}{3}$

b)

$\frac{3}{7}$

c)

$-\frac{7}{3}$

d)

$-\frac{3}{7}$

e)

$\frac{4}{7}$

17.

Solve $3^{a+3}-3^{a+2}=2\ \ \$ .

a)

$a=-2$

b)

$a=\frac{1}{2}$

c)

$a=2$

d)

No solution

18.

Solve $\left(8^y\right)^y\cdot\frac{1}{32^y}=4$ (two answers)

a)

$-\frac{1}{3}$

b)

$\frac{1}{3}$

c)

3

d)

2

e)

$-2$

19.

In a research, a type of bacteria will multiply itself in 1 minute. The amount of bacteria at the start of the research was 200. The amount of bacteria after t minutes is given by 200(2^t).Determine the time, t, in minutes for the amount of the bacteria to be 819 200.

a)

12

b)

11

c)

10

d)

13

20.

Mr. Lee invested RM 50 000 in a bank with an annual interest rate of 8%. Mr. Lee’s investment amount after t years can be determined by the formula $P=f\left(1+r\right)^t$ where f is the initial investment value and r is the annual return rate. Determine Mr. Lee's investment amount after 20 years.

a)

RM 233 048

b)

RM 203 048

c)

RM 33 048

d)

RM 30 048

Laws of indices - add math form 4

Total questions: 20

Worksheet time: 15mins

Similar Resources on Wayground