Question

Write each of the following in the product form: $43{p^{10}}{q^5}{r^{15}}$

Answer 1

Hint: First, we will see what multiplication is, Multiplicand refers to the number multiplied. The multiplier is the number that refers to the number which multiplies the first number
Power numbers can be defined to represent exactly how many times a number should be used in the process of multiplication.
Formula used: ${a^2}{a^3} = {a^{2 + 3}} \Rightarrow {a^5}$which is the power rule concept, while multiplying the same numbers of variables the power values get in addition terms.

Complete step by step answer:
Given that the product is $43{p^{10}}{q^5}{r^{15}}$, we need to find each of the products from the given form.
Since from the given, the first number is $43$ and there is no power given to this number.
Thus, we don’t need to convert into any form for this number.
Now taking the second variable ${p^{10}}$, now we can able to rewrite this using the power rule,
Thus, we get, ${p^{10}} = {p^5}{p^5}$ (separated into equal parts)
Similarly, further proceeding the same recreation, we get ${p^{10}} = {p^5}{p^5} \Rightarrow p \times p \times p \times p \times p \times {p^5}$ (the first term is separated into five times as it has the power five)
For the second term, we get, ${p^{10}} = p \times p \times p \times p \times p \times {p^5} \Rightarrow p \times p \times p \times p \times p \times p \times p \times p \times p \times p$( separated into five times as it has the power five)
Now take the second value from the given that ${q^5}$, recreating in the same way as above, we get ${q^5} = q \times q \times q \times q \times q$ is each product term.
Finally, the last term is ${r^{15}} = {r^5}{r^5}{r^5} \Rightarrow r \times r \times r \times r \times r \times {r^5} \times {r^5}$ (by the first simplification)
Similar we get, ${r^{15}} = r \times r \times r \times r \times r \times r \times r \times r \times r \times r \times r \times r \times r \times r \times r$ (fifteen times the product, while the power is fifteen)
Therefore, combining all the terms, we get, $43{p^{10}}{q^5}{r^{15}}$ can be written as in the form of
$43{p^{10}}{q^5}{r^{15}} = 43 \times p \times p \times p \times p \times p \times p \times p \times p \times p \times p \times q \times q \times q \times q \times q \times r \times r \times r \times r \times r \times r \times r \times r \times r \times r \times r \times r \times r \times r \times r$
Which is the required product form from the given.

Note: Since we used the concept of multiplication and power rules, there are several operations like addition, subtraction, and division.
The addition is the sum of two or more than two numbers, or values, or variables, and in addition, if we sum the two or more numbers a new frame of the number will be found.
The inverse of the multiplication method is called the division.
For division, like $x \times y = z$ is multiplication thus the division sees as $x = \dfrac{z}{y}$. We usually need to memorize the multiplication tables in childhood so it will help to do maths.
Subtraction operation, which is the minus of two or more than two numbers or values but here comes with the condition that in subtraction the greater number sign will stay constant.