Indices And Standard Form

1. What is

square root of 36

18

6

5

12

not-available-via-ai

Explanation

not-available-via-ai

2. What is the value of $3 squared$

6

9

8

5

not-available-via-ai

Explanation

not-available-via-ai

3. What is $10 cubed$

30

100

1000

10000

not-available-via-ai

Explanation

not-available-via-ai

4. Simplify the following:

4 to the power of 5 divided by 4 squared

=

not-available-via-ai

Explanation

not-available-via-ai

5. Simplify the following: 5^3 x 5^5

When multiplying exponents with the same base, you add the powers. In this case, 5^3 x 5^5 = 5^(3+5) = 5^8. This is a fundamental rule of exponents and is essential for simplifying expressions and solving equations involving powers.

Explanation

When multiplying exponents with the same base, you add the powers. In this case, 5^3 x 5^5 = 5^(3+5) = 5^8. This is a fundamental rule of exponents and is essential for simplifying expressions and solving equations involving powers.

6. What does the following number represent:

4.23 cross times 10 to the power of 8

423 000 000

42 300 000 000

0.000 000 042 3

423 000

The number 423 000 000 represents a quantity or value of 423 million.

Explanation

The number 423 000 000 represents a quantity or value of 423 million.

7. What is

cube root of 27

9

3

81

6

not-available-via-ai

Explanation

not-available-via-ai

8. Write the following number in standard form:6,000,000,000

The given number, 6,000,000,000, can be written in standard form as 6 x 10^9. In standard form, a number is expressed as a product of a single-digit number (between 1 and 9) and a power of 10. In this case, 6 is the single-digit number and the power of 10 is 9, indicating that the number is multiplied by 10 nine times. This form is commonly used to represent very large or very small numbers in a concise and standardized manner.

Explanation

The given number, 6,000,000,000, can be written in standard form as 6 x 10^9. In standard form, a number is expressed as a product of a single-digit number (between 1 and 9) and a power of 10. In this case, 6 is the single-digit number and the power of 10 is 9, indicating that the number is multiplied by 10 nine times. This form is commonly used to represent very large or very small numbers in a concise and standardized manner.

9. Evaluate the following:

25 to the power of 1 half end exponent

5

12.5

50

2.5

not-available-via-ai

Explanation

not-available-via-ai

10. What does the following number represent?

5.8 cross times 10 to the power of negative 5 end exponent

580 000

5 800 000

0.000 58

0.000 058

The given number, 0.000 058, represents a decimal value. Each digit after the decimal point represents a different place value. In this case, the first digit after the decimal point is in the thousandth place, the second digit is in the ten-thousandth place, and so on. Therefore, the number can be read as 58 millionths.

Explanation

The given number, 0.000 058, represents a decimal value. Each digit after the decimal point represents a different place value. In this case, the first digit after the decimal point is in the thousandth place, the second digit is in the ten-thousandth place, and so on. Therefore, the number can be read as 58 millionths.

11. Evaluate the following:

27 to the power of 2 over 3 end exponent

18

9

81

3

not-available-via-ai

Explanation

not-available-via-ai

12. Evaluate the following:

2 to the power of negative 3 end exponent

-6

-8