## clara1223 one year ago Simplify (the answer shouldn't have any negative exponents)

1. clara1223

$\left( \frac{ 3 }{ 2 } \frac{ x ^{-12}x ^{8}y ^{10} }{ x ^{5}y ^{4}y ^{-7} }\right)^{-3}$

2. Michele_Laino

If we apply the rules of multiplication and division of power with same basis, we get: $\Large {\left( {\frac{3}{2}{x^{ - 12 + 8 - 5}}{y^{10 - 4 - \left( { - 7} \right)}}} \right)^{ - 3}}$

3. Michele_Laino

4. nincompoop

First, focus on the exponents. then we apply one of the laws of exponents, which generally has the form: $$\huge (\frac{p^n}{q^m})^r = \frac{p^{n+r}}{q^{n+r}}$$

5. nincompoop

CAN you perform the indicated operation for the exponent portion in your problem?

6. clara1223

@nincompoop no, I don't know much about exponential equations

7. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @nincompoop First, focus on the exponents. then we apply one of the laws of exponents, which generally has the form: $$\huge (\frac{p^n}{q^m})^r = \frac{p^{n+r}}{q^{n+r}}$$ $$\color{blue}{\text{End of Quote}}$$ n+r or n times r mhm i guess you meant $\huge\rm (\frac{ p^n }{ p^m })^r = \frac{ p^{nr} }{ q^{mr} }$ ??

8. clara1223

so do I multiply all of the exponents and the 3/2 in the parentheses by -3?

9. clara1223

(i meant give 3/2 an exponent of -3)

10. Nnesha

when you multiply same bases then you should add their expnents you need to know exponent rules first one is $\huge\rm \frac{ x^m }{ x^n } = x^{m-n}$ if there are same bases at the numerator and at the denominator move exponent frm bottom to top or top to bottom(remember there shouldn't be any negative exponent) 2nd rule $\huge\rm (\frac{ x^m }{ y^n })^r = \frac{ x^{m \times r} }{ y^{n \times r}}$ 3rd one is $\huge\rm { x^{-m} }={ \frac{ 1 }{ x^m } }$

11. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @clara1223 (i meant give 3/2 an exponent of -3) $$\color{blue}{\text{End of Quote}}$$ yep $(\frac{ 3 }{ 2 })^{-3}$