Question 1

What is the value of $2^{-3}$?

Accepted Answer

To find the value of $2^{-3}$, we use the negative exponent law: $a^{-m} = \frac{1}{a^m}$. Therefore, $2^{-3} = \frac{1}{2^3} = \frac{1}{8}$.

Question 2

What is the value of $(3^0 + 4^{-1}) 	imes 2^2$?

Accepted Answer

Using the laws of exponents, $3^0 = 1$ and $4^{-1} = \frac{1}{4}$. So, $(3^0 + 4^{-1}) = (1 + \frac{1}{4}) = \frac{5}{4}$. Multiplying by $2^2$ (which is 4): $\frac{5}{4} 	imes 4 = 5$.

Question 3

Evaluate: $(\frac{1}{2})^{-2} + (\frac{1}{3})^{-2} + (\frac{1}{4})^{-2}$

Accepted Answer

Using the rule $(\frac{a}{b})^{-m} = (\frac{b}{a})^m$, we get: $(\frac{1}{2})^{-2} = 2^2 = 4$, $(\frac{1}{3})^{-2} = 3^2 = 9$, and $(\frac{1}{4})^{-2} = 4^2 = 16$. Adding them together: $4 + 9 + 16 = 29$.

Question 4

What is the multiplicative inverse of $5^{-3}$?

Accepted Answer

The multiplicative inverse of a number is what multiplies by it to give 1. For $5^{-3}$, the inverse is $\frac{1}{5^{-3}} = 5^3 = 125$.

Question 5

Simplify and write the answer in exponential form: $(-4)^5 \div (-4)^8$

Accepted Answer

Using the quotient law of exponents $a^m \div a^n = a^{m-n}$, we get: $(-4)^{5-8} = (-4)^{-3}$.

Exponents and Powers