\frac{(-7)^0 \times 7^9}{(-7)^2(-7)^3(-7)}
Answer (1)
Simplify the numerator: ( − 7 ) 0 = 1 , so the numerator is 7 9 .
Simplify the denominator: ( − 7 ) 2 ( − 7 ) 3 ( − 7 ) = ( − 7 ) 6 = 7 6 .
Rewrite the expression: 7 6 7 9 .
Simplify using exponent rules: 7 9 − 6 = 7 3 = 343 .
Explanation
Understanding the Expression We are asked to simplify the expression ( − 7 ) 2 ( − 7 ) 3 ( − 7 ) ( − 7 ) 0 × 7 9 . Let's break it down step by step.
Simplifying the Numerator First, we simplify the numerator. We know that any non-zero number raised to the power of 0 is 1. Therefore, ( − 7 ) 0 = 1 . So, the numerator becomes 1 × 7 9 = 7 9 .
Simplifying the Denominator Next, we simplify the denominator. We have ( − 7 ) 2 ( − 7 ) 3 ( − 7 ) . Using the exponent rule a m a n = a m + n , we can rewrite this as ( − 7 ) 2 + 3 + 1 = ( − 7 ) 6 .
Rewriting the Expression Now, we rewrite the entire expression as ( − 7 ) 6 7 9 . Since ( − 7 ) 6 = 7 6 (because a negative number raised to an even power is positive), the expression becomes 7 6 7 9 .
Applying the Exponent Rule Using the exponent rule a n a m = a m − n , we simplify the expression further: 7 6 7 9 = 7 9 − 6 = 7 3 .
Calculating the Final Value Finally, we calculate 7 3 = 7 × 7 × 7 = 49 × 7 = 343 . Therefore, the simplified expression is 343.
Examples
Understanding exponents and simplification is crucial in many areas, such as calculating compound interest. For example, if you invest money that grows at a certain percentage annually, you can use exponents to determine the future value of your investment. Simplifying expressions makes these calculations easier and more manageable.
