Rewrite 2 x 2 x 2 x 2 using an exponent
The correct Answer and Explanation is:
The expression ( 2 \times 2 \times 2 \times 2 ) can be rewritten using an exponent as ( 2^4 ). This means that 2 is multiplied by itself four times.
Explanation
Exponents are a shorthand way to express repeated multiplication of the same number. In this case, the number being multiplied repeatedly is 2, and it is multiplied by itself four times. The base is the number being multiplied (in this case, 2), and the exponent (in this case, 4) tells you how many times the base is multiplied.
Breakdown:
- ( 2^1 ) means 2 is multiplied by itself once, which is just 2.
- ( 2^2 ) means ( 2 \times 2 = 4 ).
- ( 2^3 ) means ( 2 \times 2 \times 2 = 8 ).
- ( 2^4 ) means ( 2 \times 2 \times 2 \times 2 = 16 ).
Thus, ( 2^4 = 16 ).
The exponent tells us how many times we multiply the base by itself. In this case, we multiplied 2 four times, so we write it as ( 2^4 ). This makes the expression much simpler and easier to manage, especially with larger numbers or longer strings of repeated multiplication.
Exponents are widely used in various fields like mathematics, physics, and engineering to represent large numbers or repetitive calculations more compactly. For instance, in scientific notation, exponents are used to express very large or small numbers efficiently, like ( 10^6 ) for one million.
Understanding exponents is essential for tackling more complex math topics such as algebra, where powers of numbers frequently occur, and for simplifying calculations.