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Here is some practice with natural exponents on negative bases. The expectation is that readers can make these calculations here without a calculator.

Compute $(-8)^2\text{.}$

Calculate the power $(-1)^{203}\text{.}$

Find $(-3)^3\text{.}$

Calculate $-5^2\text{.}$

Solution

Since $8^2$ is $64$ and we are raising a negative number to an even power, the answer is positive: $64\text{.}$

Since $1^{203}$ is $1$ and we are raising a negative number to an odd power, the answer is negative: $-1\text{.}$

Since $3^{3}$ is $27$ and we are raising a negative number to an odd power, the answer is negative: $-27\text{.}$

Careful: here we are raising positive $5$ to the second power to get $25$ and then negating the result: $-25\text{.}$ Since we don’t see “ $(-5)^2\text{,}$ ” the answer is not positive $25\text{.}$