power to a power rule
(a^m)^n = a^m*nIf an exponent is raised to another exponent, multiply the exponent
The power to a power rule states that when a power is raised to another power, we can simplify the expression by multiplying the exponents. Mathematically, it can be represented as:
(a^m)^n = a^(m*n)
This rule is applicable to any real number ‘a’ and positive integers ‘m’ and ‘n’. Let’s look at some examples:
Example 1:
Simplify (5^3)^2
Solution:
Using the power to a power rule, we can write:
(5^3)^2 = 5^(3*2) = 5^6
Therefore, (5^3)^2 simplifies to 5^6.
Example 2:
Simplify (x^2)^4
Solution:
Using the power to a power rule, we can write:
(x^2)^4 = x^(2*4) = x^8
Therefore, (x^2)^4 simplifies to x^8.
Example 3:
Simplify (4^2)^3
Solution:
Using the power to a power rule, we can write:
(4^2)^3 = 4^(2*3) = 4^6
Therefore, (4^2)^3 simplifies to 4^6.
In all these examples, we applied the power to a power rule to simplify the expression by multiplying the exponents. This rule is particularly useful in simplifying complex expressions involving powers.
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