The given expression is a fraction raised to a power and will be solved by multiplication of exponents for both numerator and denominator.
When in an expression, the base is a fraction raised to a number (exponent), the exponent is applied to both numerator and denominator.
In this case, the base is x^-2/3/y^-1/3 and the exponent is 15.
Since (x^a)^b=x^ab
Multiplying the exponent to both numerator and denominator,
(x^⁻²/₃/y^⁻¹/₃)^¹⁵=x^⁻²/₃*15/y^⁻¹/₃*15
Simplifying,
x^⁻²/₃*15/y^⁻¹/₃*15=x^-10/y^-5
Since both numerator and denominator have negative exponents, it is not yet in the simplest form.
According to negative exponents rule, x^-a=1/x^a
To remove the negative exponent, the fraction should be reversed.
x^-10/y^-5=y^5/x^10
The simplest form of the expression (x^⁻²/₃/y^⁻¹/₃)^¹⁵ is y^5/x^10
Learn more about multiplication of exponents:
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