Solve (y^-2/3y^-7)^-3

$$( \frac { y ^ { - 2 } } { 3 y ^ { - 7 } } ) ^ { - 3 }$$

Evaluate

$$\frac{27}{y^{15}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\left(\frac{y^{5}}{3}\right)^{-3}$$

To raise \frac{y^{5}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(y^{5}\right)^{-3}}{3^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -3 to get -15.

$$\frac{y^{-15}}{3^{-3}}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{y^{-15}}{\frac{1}{27}}$$

Divide y^{-15} by \frac{1}{27} by multiplying y^{-15} by the reciprocal of \frac{1}{27}.

$$y^{-15}\times 27$$

Expand

$$\frac{27}{y^{15}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\left(\frac{y^{5}}{3}\right)^{-3}$$

To raise \frac{y^{5}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(y^{5}\right)^{-3}}{3^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -3 to get -15.

$$\frac{y^{-15}}{3^{-3}}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{y^{-15}}{\frac{1}{27}}$$

Divide y^{-15} by \frac{1}{27} by multiplying y^{-15} by the reciprocal of \frac{1}{27}.

$$y^{-15}\times 27$$