Find the value of the expression:
$10 a^2 b^0 \text { for } a=-3, b=-8$
Answer (2)
Substitute a = − 3 and b = − 8 into the expression 10 a 2 b 0 .
Simplify ( − 3 ) 2 to 9 and ( − 8 ) 0 to 1 .
Multiply the values: 10 × 9 × 1 = 90 .
The value of the expression is 90 .
Explanation
Understanding the Problem We are given the expression 10 a 2 b 0 and the values a = − 3 and b = − 8 . Our goal is to find the value of the expression when we substitute these values for a and b .
Substituting the Values First, we substitute the given values into the expression: 10 a 2 b 0 = 10 × ( − 3 ) 2 × ( − 8 ) 0
Simplifying the Expression Next, we simplify the expression. Recall that any non-zero number raised to the power of 0 is 1. Therefore, ( − 8 ) 0 = 1 . Also, ( − 3 ) 2 = ( − 3 ) × ( − 3 ) = 9 . So we have: 10 × ( − 3 ) 2 × ( − 8 ) 0 = 10 × 9 × 1
Calculating the Final Value Finally, we multiply the numbers together: 10 × 9 × 1 = 90 Therefore, the value of the expression 10 a 2 b 0 when a = − 3 and b = − 8 is 90.
Examples
Imagine you are calculating the area of a rectangle where the length is related to a 2 and a scaling factor involves b 0 . If a = − 3 represents a transformation factor and b = − 8 is a normalization constant, then 10 a 2 b 0 might represent a scaled area. This type of calculation is fundamental in fields like physics, where you might be scaling quantities based on experimental parameters. For example, in image processing, a could represent a pixel shift, and b ensures the intensity remains within bounds.
The value of the expression 10 a 2 b 0 for a = − 3 and b = − 8 is 90 . This result is obtained by substituting the values, simplifying the terms, and performing the multiplication. Therefore, the final outcome is 90 .
;
