Question

Simplify (the answer shouldn't have any negative exponents)

Answer 1

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

Answer 2

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

Answer 3

please simplify

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

\(\color{blue}{\text{Originally Posted by}}\) @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
\[\huge\rm (\frac{ p^n }{ p^m })^r = \frac{ p^{nr} }{ q^{mr} }\]
??

Answer 8

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

Answer 9

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

Answer 10

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 \[\huge\rm { x^{-m} }={ \frac{ 1 }{ x^m } }\]

Answer 11

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