Indices And Scientific Notation Homework Task

Explanation
The base of a number system refers to the number of unique digits used to represent numbers in that system. In this expression, the base is 5 because there are 5 unique digits used in the number 57, which are 0, 1, 2, 3, and 4.

Explanation
The given expression is 2-5. In this expression, the index refers to the position of the numbers. The number 2 is at index 0 and the number 5 is at index 1. Therefore, the correct answer is -5, which is the number at index 1 in the expression.

Explanation
The scientific notation 5.4 x 10^12 indicates a large number because the exponent 12 represents the number of zeros after the decimal point. In scientific notation, the number is expressed as a decimal between 1 and 10 multiplied by a power of 10. In this case, the number 5.4 is multiplied by 10 raised to the power of 12, indicating that there are 12 zeros after the decimal point, making it a very large number.

Explanation
The scientific notation 2.3 x 10-8 indicates a small number because the negative exponent (-8) means that the decimal point is shifted 8 places to the left. This means that the number is divided by 10 raised to the power of 8, resulting in a very small value.

Explanation
The number 36 can be expressed as 3 multiplied by itself 6 times.

Explanation
The given answer, "a8," is the correct answer because it is the only option that is present in the given equation. The equation shows that the product of a3 and a5 is equal to a8. Since a8 is the only option listed in the equation, it must be the correct answer.

Explanation
The given expression is a multiplication of two terms, -3d2 and -2d3. When multiplying two terms with the same variable, we add the exponents and multiply the coefficients. In this case, the coefficients are -3 and -2, which when multiplied give us 6. The variables have exponents of 2 and 3, so when multiplied we get d5. Therefore, the correct answer is 6d5.

Explanation
The expression -6 x (-3)0 simplifies to -6. Any number raised to the power of 0 equals 1, so (-3)0 equals 1. When we multiply -6 by 1, the result is still -6.

Explanation
The given expression is a division of -xy2z3 by xyz2. When dividing, we subtract the exponents of the variables in the numerator from the exponents of the variables in the denominator. In this case, the x term cancels out because the exponent in the numerator is 2 and in the denominator is 1. The y term remains with an exponent of 1, and the z term cancels out because the exponent in the numerator is 3 and in the denominator is 2. Therefore, the simplified expression is -yz.

Explanation
The given question is asking for the square of 520. To find the square of a number, we multiply the number by itself. So, 520 multiplied by 520 is equal to 270,400. However, the correct answer given is 540, which is not the square of 520. Therefore, the given question is incomplete or not readable, and an explanation cannot be generated.

Explanation
The given equation is (d8)2 x (d7)2 = d16 x d14 = d30. This equation shows that when we square the value of d8 and multiply it by the square of d7, we get the same result as when we multiply d16 by d14. Therefore, the correct answer is d16 x d14 = d30.

Explanation
The given answer, a1, is correct because when you multiply a number by 1, the result is always the original number. In this case, a multiplied by 1 is equal to a.

Explanation
The given expression involves multiplication and division of variables and numbers. To simplify the expression, we can first simplify the exponents inside the parentheses. (2x4)3 becomes 23x12, and (x2)3 becomes x6. Then, we can divide 23x12 by x6, which results in 2x6. Therefore, the correct answer is 8x6.

Explanation
To multiply numbers in scientific notation, you multiply the coefficients and add the exponents. In this case, multiplying 7.56 by 2.63 gives you 19.9248. The exponents are 3 and -7, so you add them to get -4. Therefore, the answer is 1.98828 x 10-4.

Explanation
The given number, 0.000 000 055, can be expressed in scientific notation as 5.5 x 10-8. This is because when converting a number to scientific notation, we move the decimal point to the right until there is only one non-zero digit to the left of the decimal point. In this case, the decimal point is moved 8 places to the right, resulting in 5.5. The exponent is negative since the original number is less than 1, and the absolute value of the exponent is the number of places the decimal point was moved. Therefore, the correct scientific notation for the given number is 5.5 x 10-8.

Explanation
The given number, 147,500,000, can be expressed in scientific notation as 1.475 x 10^8. In scientific notation, a number is written as a product of a decimal number between 1 and 10, and a power of 10. In this case, 1.475 is the decimal number and 10^8 represents the power of 10. This notation is used to represent very large or very small numbers more conveniently and compactly.

Explanation
The given number, 5.2789 x 10^6, is written in scientific notation. In scientific notation, a number is expressed as a product of a decimal number between 1 and 10 and a power of 10. To convert this to an ordinary number, we need to move the decimal point 6 places to the right, as indicated by the exponent 6. This gives us the number 5 278 900, which is the correct answer.

Explanation
The given answer, 2 x 10-4, is correct. This is because the smaller the value of the exponent, the smaller the number. In this case, 10-4 is smaller than 10-3, indicating that the thickness of a sheet of paper (2 x 10-4 m) is thinner than the thickness of cellophane (2 x 10-3 m).

Explanation
The given answer is 1.8 x 10-3. This means that the thickness of the first sheet is 1.8 times 10 to the power of -3. In scientific notation, this represents a very small number. The second sheet, on the other hand, is 1.8 times 10 to the power of 0, which is equal to 1. This means that the second sheet is thicker than the first sheet by a factor of 10 to the power of 3.