Exponent Flashcards

1. 104 is not equal to which of the following?

Answer: 100,000

The expression 10⁴ means 10 multiplied by itself four times, which equals 10,000. We need to identify the option that is not equal to this value. Option A, 100,000, is equal to 10⁵. Option B, 0.1 x 10⁵, simplifies to 10,000. Option C is the expanded form of 10⁴, and Option D, 10² x 10², equals 10^(2+2) = 10⁴ due to exponent rules. Option E is simply 10,000. Therefore, 100,000 is the only option not equal to 10⁴.

2. Multiply 104 by 102

Answer: 106

When multiplying exponential terms with the same base, the rule is to add their exponents while keeping the base the same. In this problem, we are multiplying 10⁴ by 10². Applying the rule, we add the exponents 4 and 2, resulting in 10^(4+2), which simplifies to 10⁶.

3. Divide x5 by x2

Answer: x3

When dividing exponential terms with the same base, the rule is to subtract the exponent of the denominator from the exponent of the numerator, while keeping the base the same. For x⁵ divided by x², we subtract 2 from 5, which results in x^(5-2). Therefore, the simplified expression is x³.

4. Find 8.23 x 109

Answer: 8230000000

To convert a number from scientific notation (8.23 x 10⁹) to standard form, you move the decimal point. A positive exponent of 9 indicates that the decimal point should be moved 9 places to the right. Starting with 8.23, moving the decimal two places past the 3 uses two of the exponent's value, leaving seven more places. Therefore, you add seven zeros after the 3, resulting in 8,230,000,000.

5. 83,000 equals:

Answer: 8.3 x 104

To express 83,000 in scientific notation, the goal is to write it as a number between 1 and 10 multiplied by a power of 10. Start by placing the decimal point after the first non-zero digit, which gives 8.3. Then, count how many places the decimal point had to move from its original position (after the last zero in 83,000) to its new position. The decimal moved 4 places to the left, so the exponent of 10 is positive 4. Thus, 83,000 equals 8.3 x 10⁴.

6. .00875 equals:

Answer: 8.75 x 10-3

To convert the decimal 0.00875 into scientific notation, the number must be expressed as a value between 1 and 10 multiplied by a power of 10. Move the decimal point to the right until it is after the first non-zero digit, which makes the number 8.75. Since the decimal point was moved 3 places to the right, the exponent of 10 will be negative 3. Therefore, 0.00875 is equal to 8.75 x 10⁻³.