Question

Simplify the expression x^8y^-26/x^14y^-5*x^39y^-21 . After simplifying the given expression, the exponent of x is____ and the exponent of y is _____.

Answer 1

ANSWER

The exponent of x is -45 and the exponent of y is 0.

EXPLANATION

We want to simplify:

$\frac{ {x}^{8} { y}^{ - 26} }{ {x}^{14} {y}^{ - 5} \times {x}^{39} {y}^{ - 21} }$

Recall and use

${a}^{m} \times {a}^{n} = {a}^{m + n}$

$= \frac{ {x}^{8} { y}^{ - 26} }{ {x}^{14 + 39} {y}^{ - 5 + - 21} }$

$= \frac{ {x}^{8} { y}^{ - 26} }{ {x}^{53} {y}^{ - 26} }$

Also recall and apply,

$\frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$

$={x}^{8 - 53} { y}^{ - 26 - - 26}$

$={x}^{ - 45} { y}^{ 0}$

The exponent of x is -45 and the exponent of y is 0.