Final answer:
The expression '8 to the 2nd power' refers to 82, which equals 64, not 16. The standard form typically discusses scientific notation involving powers of ten, where numbers are expressed as a base of 10 raised to an exponent. Understanding and working with this standard form is important in mathematics and scientific calculations.
Step-by-step explanation:
Understanding the Standard Form of Powers
The question relates to why the standard form of 8 to the 2nd power is not equal to 16. First, we need to clarify that the expression '8 to the 2nd power' should be understood as 82, which is equal to 8 × 8, resulting in 64. The standard form refers to the method of representing numbers, especially when working with very large or very small values in scientific notation, which is a base of 10 raised to an exponent. For example, 1.6 × 102 is in standard form and is equal to 160 when the decimal point is moved two places to the right due to the exponent 2. When dealing with negative exponents, like in 2.4 × 10-2, we move the decimal left by the exponent, resulting in the value 0.024.
Mathematics allows various methods to arrive at the same answer, and manipulating powers of ten is a common practice in scientific notation. For instance, when dividing 2.4 × 1013 by 8 × 107, several approaches can be taken. One might subtract the exponents directly, with the result being 24 × 106. Alternatively, transforming the divisor gives us 0.125 × 10-7, which when multiplied with 2.4 × 1013 gives us the same result.
Being able to work with standard form and understand exponents is essential for solving problems efficiently, especially in scientific calculations. The use of proper notation ensures clarity and helps in recognizing patterns such as the powers-of-ten notation originating from the decimal counting system based on our ten fingers.