Rewrite 9×9×9×9 using an exponent.
The Correct Answer and Explanation is :
The expression ( 9 \times 9 \times 9 \times 9 ) can be rewritten using exponents as ( 9^4 ).
Explanation:
In mathematics, exponents are a shorthand way of expressing repeated multiplication of the same number. The general form for an exponent is ( a^n ), where:
- ( a ) is the base,
- ( n ) is the exponent, which indicates how many times the base is multiplied by itself.
In the expression ( 9 \times 9 \times 9 \times 9 ), we see that the number 9 is being multiplied together four times. Thus, the exponent ( 4 ) represents the number of times the base ( 9 ) is multiplied by itself.
To illustrate this further, let’s break down the process of rewriting the expression with an exponent:
- Identify the Base: Here, the base is ( 9 ).
- Count the Factors: We have four factors of ( 9 ) in the multiplication.
- Write the Exponential Form: Since we have four ( 9 )s being multiplied, we can express this as ( 9^4 ).
Now, let’s calculate ( 9^4 ):
[
9^4 = 9 \times 9 \times 9 \times 9
]
Calculating it step-by-step:
- First, calculate ( 9 \times 9 = 81 ).
- Next, take that result and multiply it by ( 9 ): ( 81 \times 9 = 729 ).
- Finally, multiply ( 729 ) by ( 9 ) again: ( 729 \times 9 = 6561 ).
Thus, ( 9^4 = 6561 ).
In summary, the expression ( 9 \times 9 \times 9 \times 9 ) can be succinctly rewritten as ( 9^4 ), which equals ( 6561 ). Using exponents not only simplifies expressions but also makes calculations more manageable, particularly when dealing with larger numbers or more complex mathematical problems.