Question

tell whether you will add, subtract, or multiply the exponents. then simplify by finding the value of the expression.

1. \\(\frac{3^6}{3^3}\\) \\(\to\\)
2. \\(8^2 \bullet 8^{-3}\\) \\(\to\\)
3. \\((3^2)^3\\) \\(\to\\)
4. \\(5^3 \bullet 5^1\\) \\(\to\\)
5. \\(\frac{4^2}{4^4}\\) \\(\to\\)
6. \\((6^2)^2\\) \\(\to\\)

Explanation:

Problem 1: $\boldsymbol{\frac{3^6}{3^3}}$

Step1: Identify exponent rule

For $\frac{a^m}{a^n}$, use quotient rule: subtract exponents. So $m - n = 6 - 3 = 3$.

Step2: Simplify the expression

$3^{6 - 3} = 3^3 = 27$.

Step1: Identify exponent rule

For $a^m \cdot a^n$, use product rule: add exponents. So $m + n = 2 + (-3) = -1$.

Step2: Simplify the expression

$8^{2 + (-3)} = 8^{-1} = \frac{1}{8}$.

Step1: Identify exponent rule

For $(a^m)^n$, use power - of - a - power rule: multiply exponents. So $m\times n = 2\times3 = 6$.

Step2: Simplify the expression

$(3^2)^3=3^{2\times3}=3^6 = 729$.

Answer:

Subtract, value is 27

Problem 2: $\boldsymbol{8^2 \cdot 8^{-3}}$