Solve (-2)^5*(-2)^-7=4^-2

$$( - 2 ) ^ { 5 } \times ( - 2 ) ^ { - 7 } = 4 ^ { - 2 }$$

Verify

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and -7 to get -2.

$$\left(-2\right)^{-2}=4^{-2}$$

Calculate -2 to the power of -2 and get \frac{1}{4}.

$$\frac{1}{4}=4^{-2}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{1}{4}=\frac{1}{16}$$

Least common multiple of 4 and 16 is 16. Convert \frac{1}{4} and \frac{1}{16} to fractions with denominator 16.

$$\frac{4}{16}=\frac{1}{16}$$

Compare \frac{4}{16} and \frac{1}{16}.

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