Free Printable Roots and Powers Revision

1.

Which expression represents 1/9⁶ using a negative exponent?

a)

-6^-9

b)

-9^-6

c)

9^-6

d)

6^-9

2.

Which expression is equivalent to (5⁴)(5^-5)?

a)

-1/5

b)

1/5⁹

c)

1/5

d)

5⁰

3.

An astronomer finds that the diameter of asteroid A is roughly 10^-3 kilometers, whereas the diameter of asteroid B is roughly 10⁶ kilometers. About how many times as great is the diameter of asteroid B than asteroid A?

a)

10^-3

b)

10³

c)

10⁹

d)

10⁹¹⁸

4.

Bacteria are among the smallest living things. Some of the largest bacteria measure 7.87 x 10^-5 of an inch across. Which value expresses this number in standard form?

a)

0.0000787

b)

0.000787

c)

0.00787

d)

787,000

5.

The average weight of an African elephant is 1.44 x 10⁴ pounds and that of a white rhinoceros is 7.94 x 10³ pounds. What is the approximate difference in weight of these two animals?

a)

2.23 x 10⁴ pounds

b)

6.46 x 10³ pounds

c)

6.5 x 10¹ pounds

d)

9.38 x 10⁷ pounds

6.

You have a square with an area of 49 in². If you cut off 1 inch from each side. What would the area of the new square be?

a)

45 in²

b)

36 in²

c)

25 in²

d)

30 in²

7.

Evaluate the following expression. (Remember the Order of Operations)

a)

21

b)

10

c)

11

d)

19

8.

Evaluate $\left(\frac{16}{81}\right)^{-\frac{3}{4}}$

a)

$3\frac{3}{8}$

b)

$\frac{3}{8}$

c)

$1\frac{11}{16}$

d)

$\frac{8}{27}$

9.

Calculate the value of $\frac{5.98\times10^8+4.32\times10^{9\ \ \ }}{6.14\times10^{-2}}$ Give your answer in standard form correct to 3 significant figures.

a)

$8.0098\times10^{10}$

b)

$8.01\times10^{10}$

c)

$8.01\times10^6$

d)

$8.0098\times10^6$

10.

$y^2=\frac{ab}{a+b},\ a\ =\ 3\times10^8,\ b\ =\ 2\times10^7$ . Find the value of y and give your answer in standard form correct to 2 significant figures.

a)

$1.9\times10^7$

b)

$4.3\times10^6$

c)

$1.875\times10^7$

d)

$4.3\times10^3$

11.

The number 1104 can be written as $3\times2^c\times d$ , Work out the value of c and d

a)

c = 5, d = 23

b)

c = 4, d = 32

c)

c = 4, d = 23

d)

c = 5, d = 32

12.

Eddie owns three motorcycles. He cleans the Harley once every 8 days, the Honda once every 10 days and the Kawasaki once every 15 days. Today, he cleaned all three motorcycles, after how many days will he next clean all three motorcycles on the same day again?

(a)

13.

Solve for x $4^{5x}\div\left(2^{3x}\right)^2=256$

a)

4

b)

3

c)

$\frac{1}{2}$

d)

2

14.

Without using mathematical tables or a calculator, evaluate $27^{\frac{2}{3}}\times\left(\frac{81}{16}\right)^{-\frac{1}{4}}$

a)

2

b)

6

c)

3

d)

12

Roots and Powers Revision

Total questions: 14

Worksheet time: 44mins

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