simplify (x^4/y^3)^-3
To simplify \((x^4/y^3)^{-3}\), we can apply the power rule for exponents.
First, let's simplify the expression within the parentheses:
\((x^4/y^3)^{-3} = (x^4)^{-3} / (y^3)^{-3}\)
Applying the power rule for exponents, we multiply the exponents inside the parentheses by -3:
\(x^{4 \cdot -3} / y^{3 \cdot -3} = x^{-12} / y^{-9}\)
Using the property that \(a^{-n} = 1/a^n\) for any non-zero number \(a\):
\(1/x^{12} / 1/y^{9} = y^9/x^{12}\)
Therefore, \((x^4/y^3)^{-3}\) simplifies to \(y^9/x^{12}\).
To simplify the expression ${(x^4/y^3)}^{-3}$, we can apply the power of a quotient rule.
First, let's remember that raising a power to another power means multiplying the exponents, and that a negative exponent can be converted to a positive exponent by moving the term to the denominator.
Applying these rules, we have:
${(x^4/y^3)}^{-3} = \left(\frac{x^4}{y^3}\right)^{-3}
= \frac{1}{\left(\frac{x^4}{y^3}\right)^3}
= \frac{1}{\frac{x^4 \cdot x^4 \cdot x^4}{y^3 \cdot y^3 \cdot y^3}}
= \frac{1}{\frac{x^{4+4+4}}{y^{3+3+3}}}
= \frac{1}{\frac{x^{12}}{y^9}}
= \frac{1 \cdot y^9}{x^{12}}
= \frac{y^9}{x^{12}}$
Therefore, the simplified expression is $\frac{y^9}{x^{12}}$.
To simplify the expression (x^4/y^3)^-3, we need to apply the power rule for exponents. According to the rule, when raising a power to another power, we multiply the exponents.
In this case, we have (x^4/y^3)^-3. To simplify, we multiply the exponent of x by the -3 and the exponent of y by -3:
(x^4)^(-3) / (y^3)^(-3)
Applying the power rule, we have:
x^(4 * -3) / y^(3 * -3)
Simplifying further:
x^(-12) / y^(-9)
Now, remember that any term with a negative exponent can be rewritten by taking its reciprocal and changing the exponent to positive. So, we can rewrite the expression as:
y^9 / x^12
Therefore, the simplified form of (x^4/y^3)^-3 is y^9 / x^12.