Question

Evaluate without using a calculator (x2y-3)0+x1/3-(4x)1/2 when x = 64 and y = 27. Show work.

Answer 1

Given:

The expression is:

$(x^2y-3)^0+x^{\frac{1}{3}}-(4x)^{\frac{1}{2}}$

To find:

The value of the given expression when $x=64$ and $y=27$.

Solution:

We have,

$(x^2y-3)^0+x^{\frac{1}{3}}-(4x)^{\frac{1}{2}}$

Putting $x=64$ and $y=27$, we get

$=((64)^2(27)-3)^0+(64)^{\frac{1}{3}}-(4(64))^{\frac{1}{2}}$

It can be written as

$=((64)^2(27)-3)^0+(4^3)^{\frac{1}{3}}-(4)^{\frac{1}{2}}(64)^{\frac{1}{2}}$

$=1+4-2(8)$           $[\because a^0=1,a\neq 0]$

$=5-16$

$=-11$

Therefore, the value of the given expression $-11$ when $x=64$ and $y=27$.