Evaluate: $2^4$
Simplify: $7^0$
Find the value of: $5^{-1}$
Express using positive exponent and simplify: $4^{-3}$
Simplify: $(\frac{3}{5})^{-2}$
Evaluate: $(\frac{2}{3})^3$
Simplify: $\frac{6^{-2}}{6^{-4}}$
Find the value of: $(-1)^6$
Find the value of: $(-1)^9$
Simplify: $(\frac{5}{2})^{-1}$
Explanation: This means multiplying the base ($2$) by itself $4$ times.
Calculation: $2 \times 2 \times 2 \times 2 = 16$.
Explanation: According to the Zero Exponent Rule, any non-zero number raised to the power of $0$ is always $1$.
Calculation: $1$.
Explanation: A negative exponent indicates a reciprocal. $a^{-n} = \frac{1}{a^n}$.
Calculation: $\frac{1}{5^1} = \frac{1}{5}$.
Explanation: First, flip the base to the denominator to make the exponent positive, then calculate the cube of $4$.
Calculation: $\frac{1}{4^3} = \frac{1}{4 \times 4 \times 4} = \frac{1}{64}$.
Explanation: To remove a negative exponent from a fraction, flip the fraction (find its reciprocal) and change the exponent to positive.
Calculation: $(\frac{5}{3})^2 = \frac{5^2}{3^2} = \frac{25}{9}$.
Explanation: Apply the power to both the numerator and the denominator.
Calculation: $\frac{2^3}{3^3} = \frac{2 \times 2 \times 2}{3 \times 3 \times 3} = \frac{8}{27}$.
Explanation: Use the Quotient Rule ($a^m \div a^n = a^{m-n}$). Subtract the bottom exponent from the top exponent.
Calculation: $6^{-2 – (-4)} = 6^{-2 + 4} = 6^2 = 36$.
Explanation: When a negative number is raised to an even power, the result is positive because the signs cancel out in pairs.
Calculation: $1$.
Explanation: When a negative number is raised to an odd power, the result remains negative.
Calculation: $-1$.
Explanation: A power of $-1$ simply means taking the reciprocal of the fraction.
Calculation: $\frac{2}{5}$.