Evaluate (-9x) to the second power when x = 7

Mathematics is conducted by some basic operations like addition, subtraction, multiplication, etc. These operations are applicable in all the branches of mathematics somewhere or the other.

Algebra is also a branch which deals with symbols, numbers, and these basic operations for the simplification of problems.

The article given below covers the topic of algebraic expressions with their components types and some suitable examples. It also contains some problems related to the power of a variable.

Algebraic Expressions

Algebraic expressions are expressions that mainly consist of constants, variables, and coefficients. And, these three components are associated with each other by the means of various algebraic operations.

Components of Algebraic operations

• Constants: They are the real numbers known values of the expression.
• Variables: They are the unknown values represented by alphabetical letters.
• Coefficients: They are the integers associated with variables.

Types of Expressions 

The algebraic expressions are divided into three on the basis of the number of variables.

• Monomial expressions: These are the expressions with one variable. For example 2x,2y,etc.
• Binomial expression: These are the expressions with two variables. For example; 2x+8, 5y-7, etc.
• Polynomial expression: These are the expressions with multiple variables. For example xy+yz+zx, ab+bc+ca,etc

Some basic Algebraic Formula 

• a² – b² = (a-b)(a+b)
• (a+b)² = a² + 2ab + b²
• (a-b)² = a² – 2ab + b²
• a² + b² = (a-b)² +2ab.
• (a+b+c)² = a²+b²+c²+2ab+2ac+2bc.
• (a-b-c)² = a²+b²+c²-2ab-2ac+2bc.
• a³-b³ = (a-b) (a² + ab + b²)
• a³+b³ = (a+b) (a² – ab + b²)

Evaluate (-9x) to the second power when x=7.

Solution:

The word equation (-9x) to the second power can be written as 

=>(-9x)²

which can also be written as

=>(-9x) . (-9x)

=>81x²

Now, we have x = 7

=>81 × (7)²

=>81 × 49

=> 3969

Sample Problems 

Question 1. What is x to the power of 2?

Answer:

x to the power of 2 can be expressed as x² in algebraic expression form.

Question 2. How to express x to the power of 3?

Answer:

x to the power of 3 can be written as x³.

For example, if x=2 then x³ = (2)³

                                           = 8

Question 3. Express the given numbers as a power of the second.

(i) 25          (ii) 5

Answer:

(i) 25

25 to the power of second can be written as

=>(25)²

=>625

(ii) 5 

5 to the power of second can be written as

=>(5)²

=>25

Question 4. Express the numbers as a power of 3.

(i)9       (ii)4

Answer:

(i) 9

9 to the power of 3 can be written as 

=>(9)³

=> 729

(ii) 4

4 to the power of 3 can be written as 

=>(4)³

=> 64