3. What makes the statement true? 7^–2 =?
4. Evaluate the expression 6^-2 • 4^0?
5. Write 5^2 • 5^-1 • 5^3 as a single exponent.
9. What is the solution to (4 × 10^3) × (6 × 10^6), written in scientific notation?
11. Find the product.
1/10 • 4/10
Plz help me
7^-2 = 1/7^2 = 1/49
6^-2 = 1/6^2 = 1/36
4^0 = 1 (as does any number n^0)
6^-2 • 4^0 = 1/36 * 1 = 1/36
5^2 • 5^-1 • 5^3 = 5^(2-1+3) = 5^4
(4×10^3)×(6×10^6) = 4×6×10^(3+6) = 24×10^9 = 2.4×10^10
1/10 • 4/10 = 1•4/(10•10) = 4/100 = 1/25
Thank You so so so much :D
My pleasure it is. :-)
3. To determine what makes the statement true, we need to evaluate 7^–2. The exponent –2 means that we need to find the reciprocal of the number raised to the power of 2. In this case, we need to find the reciprocal of 7^2. To do that, we square 7, which gives us 49, and then take the reciprocal of 49, which is 1/49. So, 7^–2 is equal to 1/49.
4. To evaluate the expression 6^-2 • 4^0, we need to simplify each part separately and then multiply them together. The exponent –2 means we need to find the reciprocal of 6^2. Squaring 6 gives us 36, and taking the reciprocal of 36 gives us 1/36. The exponent 0 means that 4^0 is equal to 1. Therefore, 6^-2 • 4^0 simplifies to 1/36 • 1, which is equal to 1/36.
5. To write 5^2 • 5^-1 • 5^3 as a single exponent, we need to combine the exponents. When multiplying numbers with the same base, we add the exponents. In this case, we have 5^2, 5^-1, and 5^3. Adding the exponents gives us 5^(2 + (-1) + 3). Simplifying, we get 5^4. Therefore, 5^2 • 5^-1 • 5^3 can be written as 5^4.
9. To find the solution to (4 × 10^3) × (6 × 10^6) in scientific notation, we need to multiply the numbers and then adjust the result to be in proper scientific notation form. Multiply the numbers to get 4 × 6 = 24, and 10^3 × 10^6 = 10^(3+6) = 10^9. Combine the results to get 24 × 10^9. However, in scientific notation, the coefficient should be between 1 and 10. To achieve this, we divide 24 by 10, which gives us 2.4, and multiply the exponent 10^9 by 10, which gives us 10^10. Therefore, the solution is 2.4 × 10^10 in scientific notation.
11. To find the product of 1/10 • 4/10, we multiply the numerators (1 * 4) to get 4, and multiply the denominators (10 * 10) to get 100. Therefore, the product is 4/100. Simplifying further, we divide both the numerator and denominator by their greatest common divisor, which is 4. Dividing 4 by 4 gives us 1, and dividing 100 by 4 gives us 25. So, the product simplifies to 1/25.