Trivia: Exponents, Scientific Notation, Cube Roots! Math Quiz

The given expression is 7^24, which represents the simplified exponential expression. This is because 7^24 means multiplying 7 by itself 24 times, resulting in a very large number. Therefore, the correct answer is 7^24.

The cube root of 125 is 5 because when you multiply 5 by itself three times (5 x 5 x 5), you get 125. The cube root is the number that, when multiplied by itself three times, gives the original number. Therefore, 5 is the cube root of 125.

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Product Rule for Exponents

The correct answer is 5^16 because it represents the simplified exponential expression. The base, which is 5, is raised to the power of 16, resulting in a single term with no other operations or simplifications possible.

The correct answer is 9^28. This is the simplified exponential expression because it represents the base number 9 raised to the power of 28.

The correct answer is 7^40 because it represents the simplified exponential expression. The expression 7^40 means multiplying 7 by itself 40 times, resulting in a very large number.

The cube root of a number is a value that, when multiplied by itself three times, gives the original number. In this case, if we multiply 6 by itself three times (6 x 6 x 6), we get 216. Therefore, the statement that the cube root of 216 is 6 is true.

The volume of a cube is calculated by multiplying the length of its edges three times. In this case, the volume is given as 64 inches, so we need to find the length of the edges. By taking the cube root of 64, we get 4. Therefore, the length of the edges of the cube is 4 inches.

Power rule of exponents

Product Rule

The number 1,420,000 can be expressed in scientific notation as 1.42 x 10^6. In scientific notation, the number is written as a decimal between 1 and 10 (in this case, 1.42) multiplied by a power of 10 (in this case, 10^6). This notation is used to represent very large or very small numbers in a more concise and standardized format.

The expression 99 * 97 can be written as 9^2 * 9^16. When multiplying two numbers with the same base, the exponents can be added together. Therefore, 9^2 * 9^16 simplifies to 9^18. However, none of the answer choices represent 9^18. The closest answer choice is 9^16, which is the correct answer.

The volume of a cube is calculated by multiplying the length of one of its edges by itself three times. In this case, the volume is given as 512 feet. To find the length of the edges, we need to find the cube root of the volume. The cube root of 512 is 8, so the length of each edge of the cube is 8 feet.

The given expression can be represented as a single exponential expression by adding the exponents of the same base. In this case, the base is 2 and the exponents are 16 and 16. When we add these exponents, we get 32. Therefore, the expression 2^16 * 2^16 can be simplified to 2^32.

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The given expression can be simplified by multiplying the terms inside the parentheses, which results in (9)9. This further simplifies to 81. However, none of the answer choices represent this simplified exponential expression, so the correct answer is not available.

The correct answer is (-11)^ -21. This is the simplified exponential expression because it represents raising -11 to the power of -21. The negative exponent indicates that the base (-11) should be inverted, and the positive exponent indicates how many times it should be multiplied. Therefore, (-11)^ -21 represents dividing 1 by (-11) 21 times.

The given number, 5.34 x 10^-4, is written in scientific notation. In standard form, we move the decimal point 4 places to the left because the exponent is negative. Therefore, the correct answer is 0.000534.

The expression 65 * 63 can be represented as 6^8 since both numbers can be expressed as powers of 6.

Dividing scientific notation: SUBTRACT the exponenent in the numerator from the exponent in the demoninator:
9.0 x 10^3 divided by 3.0 x 10^2 =
(9 divided by 3)x 10^(3-2)

The correct answer is 32,501,000 because it is the only option that matches the given number, 3.2501 x 10^7, when written in standard form. The other options either have additional decimal places or do not have the correct number of digits.

The hair is wider than the E. coli bacterium. The given measurements indicate that the hair is approximately 34 times wider than the bacterium.

Quotient Rule for Exponents

The given number, 0.00098, can be written in scientific notation as 9.8 x 10^-4. This is because when we move the decimal point 4 places to the right, we get 9.8. The negative exponent of -4 indicates that the decimal point has been moved to the left, making the number smaller.

The correct answer is 5.4 × 10^3, 4.5 × 10^4, 5.4 × 10^4. The numbers are arranged in order from least to greatest by comparing the coefficients (5.4 and 4.5) first. Since 4.5 is smaller than 5.4, it comes before 5.4 in the list. Then, we compare the exponents (10^3 and 10^4). 10^3 is smaller than 10^4, so it comes before 10^4 in the list. Therefore, the correct order is 5.4 × 10^3, 4.5 × 10^4, 5.4 × 10^4.

Zero Exponent Rule

2.32 x 10^3

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Quotient Rule and Negative Exponent Rule

Division: Subtract the exponents: (-2) - (-3) = +1

When multiplying with scientific notation: add the exponents.
(8.0 x 10^-2) x (3 x 10^-3) = (8 x 3)x 10^(-2 + -3) = 24 x 10^-5 = 2.4 x 10^-4

Negative Exponent Rule

When MULTIPLYING in scientific notation, ADD the exponent.
Make sure you change your answer to proper scientific notation. (3.0x 10^7) (4.0 x 10^5)= (3.0 x 4.0)x 10^(7+5)