Solve (i^-3)^-5*i^-9

$$( i ^ { - 3 } ) ^ { - 5 } \cdot i ^ { - 9 }$$

Evaluate

$$-1$$

Solution Steps

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

$$i^{15}i^{-9}$$

To multiply powers of the same base, add their exponents. Add 15 and -9 to get 6.

$$i^{6}$$

Calculate i to the power of 6 and get -1.

$$-1$$

Real Part

$$-1$$

Solution Steps

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

$$Re(i^{15}i^{-9})$$

To multiply powers of the same base, add their exponents. Add 15 and -9 to get 6.

$$Re(i^{6})$$

Calculate i to the power of 6 and get -1.

$$Re(-1)$$

The real part of -1 is -1.

$$-1$$