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erastova [34]
3 years ago
11

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

xponent of y is _____.
Mathematics
1 answer:
timama [110]3 years ago
5 0

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.

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