Exponents represent repeated multiplication, making numbers grow quickly. For example, 2 to the 3rd power means multiplying three 2's together, resulting in 8. This concept differs from multiplication, which is simply repeated addition. Understanding exponents is essential for mastering higher-level math.
Let's start by taking a look at an example evaluating $\blueD3$ squared:
$\large\blueD3^2 = \blueD3 \times \blueD3 = \greenD9$
Here's a question to make sure you got that:
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##Connection to a square
Finding $\blueD3^2$ (read as "three squared") is the same as finding the area of a square with side length $\blueD3$:
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##Practice set:
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Sal Khan considers two different ways to think about why a number raised to the zero power equals one: 1) if 2^3 = 1x2x2x2, then 2^0 = 1 times zero twos, which equals 1. 2) By following a pattern of decreasing an exponent by one by dividing by the base, we find that when we get to the 0 power, we end up dividing the base by itself, resulting in 1.
In this math activity, we arrange three math expressions from smallest to largest. We evaluate the expressions: 2 cubed minus 2, 2 squared plus 3 to the power of 0, and 3 squared. We find their values to be 6, 5, and 9. The correct order is 5, 6, and 9.
Exponents of decimals can be calculated by multiplying the decimal number by itself as many times as the exponent indicates. When multiplying decimals, count the total number of digits to the right of the decimal points in both numbers and place the same number of digits to the right of the decimal point in the product.
Raising fractions to a power is a fundamental math skill. To do this, simply multiply the numerators and denominators separately. For example, when raising a fraction like 2/3 to the third power, multiply the numerators (2 × 2 × 2 = 8) and the denominators (3 × 3 × 3 = 27) to get the result 8/27. This method applies to all powers, making it easy to understand and apply.
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