Writing expressions with exponents

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There are different types of expressions in math. An expression can be written using different variables, numbers and exponents. The exponent is the power of the number or the variables. The exponent tell the number of times the base variable or number is to be multiplied. In an exponent expression if the base value is equal then the powers of the numbers can be equated.
This rule can be written as: am = an. Hence, m = n.

Example 1: Find the value of p in the expression: 125 = 5p
Solution: Here the exponent expression is given 125 = 5p.
Hence the number can be factorized as 125 = 5 x 5 x 5.
(The number 5 is multiplied three times so 5 is raised to the power 3.)
Now the number can be written in the exponent form as: 125 = 53.
Now equating the number to the given expression: 5p = 53.
Since the base numbers for the expressions are equal equate the powers.
Hence the answer is p = 3.
Question: Multiple choice question (Pick the correct option.)
The number 81 can be written as an exponent expression as the following?
a)    93                    b) 9                 c) 92                d) None of these.
Correct answer: option c.
The number 81 can be factorized and written as: 81 = 3 x 3 x 3 x 3 = 9 x 9.
The number 9 is multiplied two times. So, 2 is the exponent for the number 9.
Hence the exponent expression for 81 = 92.

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