Definition of Power: Power of the literal refers to the repetition of a literal. The literal represents the base, and its multiplicative power represents the index. In this product, the factors are written slightly raised to the right of the quantity.
Taking the expression 'a' and multiplying it by 4, it must be:
The answer is p x p x p x p = p⁴, where ‘p’ acts as the base and the index refers to how many times it has been multiplied, and 4 is the index.
Few more examples:
(i) c × c × c has three factors so to express it we can write c × c × c = c ^ 3.
Here the symbol "^" refers to raise to the power.
(iii) z × z × z × z × z has seven factors so to express it we can write z × z × z × z × z = z^5
# How to understand the power of literal quantities in terms of reading and writing.
(i) Product of a × a is written as a^2 and it is read as a squared or a raised to the power 2.
(ii) The product of p*p*p can be viewed as either p cubed or p raise to the power 3. It is written as p^3.
(iii) Product of v × v × v × v is written as v^4 and it is read as the fourth power of v or v raised to power 4.
(iv) Product of 5 × 5 × 5 × 5 × 5 x 5 is written as 40 and it is read as the sixth power of 5 or 5 raised to the power 6.
Before we proceed further, let us understand the meaning of the literal representation of an algebraic term and literal coefficients.
The literal representation of an algebraic term and literal coefficients.
A factor containing at least one literal representation of an algebraic term in product form is referred to as a literal coefficient of the remaining factor or factors.
5a2b2c2 is an algebraic term. It is split as a product of two factors.
Consider 5 x a2b2c2
In this case, a,b, and c are the literals.
In certain instances, algebraic terms are expressed as the product of two or more components. Here 5 and a2b2c2 are the two factors multiplied with each other. In this instance, each factor is referred to as the coefficient of the remaining factor or factors. When a coefficient includes at least one literal value, it is referred to as the literal coefficient of the remaining component of factors.
Therefore, the factor a2b2c2 is called the literal coefficient of 5.
More complex examples of the power of the literal
1. p × q × b × b × b = p*q*(b^3)
2. Express 9 × p × p × p × q × q in power form.
9 × p × p × p × q × q = 9*(p^3)* (q^2)
3. Express 8 × 7 × a × b × b × v = 8 × 7 × a × b × b × v = 56*a*(b^2)*v