solve(using laws of exponent)
[(11)5/3] × (121)^-1/2 × (√11)4x/x=11
please solve it fast and correctly
unnecessary answers will result in report
I want proper ANSWER with WORKING
Answers
Step-by-step explanation:
What Is an Exponent, Anyway?
There’s nothing mysterious! An exponent is simply shorthand for multiplying that number of identical factors. So 4³ is the same as (4)(4)(4), three identical factors of 4. And x³ is just three factors of x, (x)(x)(x).
One warning: Remember the order of operations. Exponents are the first operation (in the absence of grouping symbols like parentheses), so the exponent applies only to what it’s directly attached to. 3x³ is 3(x)(x)(x), not (3x)(3x)(3x). If we wanted (3x)(3x)(3x), we’d need to use grouping: (3x)³.
Negative Exponents
A negative exponent means to divide by that number of factors instead of multiplying. So 4−3 is the same as 1/(43), and x−3 = 1/x3.
As you know, you can’t divide by zero. So there’s a restriction that x−n = 1/xn only when x is not zero. When x = 0, x−n is undefined.
A little later, we’ll look at negative exponents in the bottom of a fraction.
Fractional Exponents
A fractional exponent—specifically, an exponent of the form 1/n—means to take the nth root instead of multiplying or dividing. For example, 4(1/3) is the 3rd root (cube root) of 4.
Arbitrary Exponents
You can’t use counting techniques on an expression like 60.1687 or 4.3π. Instead, these expressions are evaluated using logarithms.
Here’s All You Need to Memorize
And that’s it for memory work. Period. If you memorize these three definitions, you can work everything else out by combining them and by counting:
x^n = (x)(x)...(x), n factors of x; x^-n = 1/(x)(x)...(x); x^(1/n) = nth root of x
Granted, there’s a little bit of hand waving in my statement that you can work everything else out. Let me make good on that promise, by showing you how all the other laws of exponents come from just the three definitions above. The idea is that you won’t need to memorize the other laws—or if you do choose to memorize them, you’ll know why they work and you’ll find them easier to memorize accurately.