Answer:
a . x = 512
b. x^1/2•y•z^5/4
Step-by-step explanation:
a. Here in this question, we want to find the value of x, given the equation.
x^2/3 = 64
Now, to find the value of x, we shall raising both powers to the reciprocal of 2/3
When we talk of reciprocal, we mean a number such that when we multiply this number by that particular number, our result is 1.
So for 2/3, the reciprocal is 3/2
So let’s raise the power of both sides to 3/2
Thus;
x^2/3(3/2) = 64^3/2
Kindly recall that 2/3(3/2) = 2/3 * 3/2 = 1
Thus ;
x = 64^3/2
So what this mean is that we will find the square root of 64 and cube our answer.
Thus;
x = {√(64)}^3
x = 8^3
x = 512
b. According to laws of indices, kindly note that
b√(a) = a^1/b
Thus;
4 √(x^2•y^4•z^5) = (x^2•y^4•z^5)^1/4
So what we do is to multiply each of the powers in the bracket by 1/4
Thus, we have the following;
x^2(1/4) • y^4(1/4) • z^5(1/4)
= x^1/2•y•z^5/4
where • simply refers to multiplication between the terms
