%5E2-without-exponents.jpeg "(x^4)^2 Without Exponents")
Understanding (x^4)^2 without Exponents
The expression (x^4)^2 can seem intimidating at first glance, but it becomes much simpler when we understand the fundamentals of exponents. Let's break it down step-by-step:
What are exponents?
Exponents are a shorthand way of representing repeated multiplication. In the expression x^n, 'x' is the base and 'n' is the exponent. This represents 'x' multiplied by itself 'n' times. For example, x^3 = x * x * x.
Applying the rules of exponents
When we have an exponent raised to another exponent, as in (x^4)^2, we can simplify it using the rule of power of a power. This rule states that (x^m)^n = x^(m*n).
Simplifying (x^4)^2
Following the rule of power of a power, we can simplify (x^4)^2 as:
(x^4)^2 = x^(4*2) = x^8
Final Answer
Therefore, (x^4)^2 is equivalent to x^8. This means we multiply 'x' by itself 8 times.
Without exponents, this expression would be written as: x * x * x * x * x * x * x * x.