The given expression is:
(23^20-53^19)/(-9)^9
This is a mathematical expression that involves multiple operations. The first step is to understand the order of operations, or PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction)
Parentheses: The expression does not contain any parentheses, so we can move on to the next step.
Exponents: The first term, 23^20, contains an exponent. The exponent operator (^) has higher precedence than the multiplication operator (), so we will simplify the exponent first. 3^20 is equal to 3 raised to the power of 20, which is equal to 3 * 3 * 3 * ... * 3 (20 times) = 59,049. Therefore, the first term is now 2 * 59,049.
The second term 5*3^19 also contains an exponent, so we simplify it in the same way as the first term. 3^19 is equal to 3 * 3 * 3 * ... * 3 (19 times) = 7,29,043. Therefore, the second term is now 5 * 7,29,043.
Multiplication and Division: After simplifying the exponents, we can see that the expression contains both multiplication and division. Since division has the same precedence as multiplication, we can simplify the expression from left to right.
The first term 2 * 59,049 is the product of 2 and 59,049. Multiplying these two numbers gives us 118,098.
The second term 5 * 7,29,043 is the product of 5 and 7,29,043. Multiplying these two numbers gives us 36,45,215.
The third term is the division of two terms. We have (23^20-53^19) / (-9)^9
Subtraction : Now we have the subtraction of two terms (118,098 - 36,45,215)
Now we have the division of two terms (-35,27,117) / (-9)^9. In this step, we are dividing the subtraction with -9 raised to the power of 9
The final step is to simplify the division. -9^9 is equal to -9 * -9 * -9 * -9 * -9 * -9 * -9 * -9 * -9 = -3486784401.
So the final expression is -35,27,117/-3486784401.
The expression is a very large negative number divided by a very large negative number, which results in a very small positive number.