Question

4 which of the following is an equivalent expression for $4^{2} \times 4^{-6}$? \
\bigcirc a. $4^{8}$ \
\bigcirc b. $4^{7}$ \
\bigcirc c. $\frac{1}{4^{4}}$ \
\bigcirc d. $\frac{1}{4^{-4}}$ \
8 which of the following equations is not true? \
\bigcirc a. $3^{6} \times 3^{-3} = 27$ \
\bigcirc b. $3^{3} \times 3^{-6} = \frac{1}{27}$ \
\bigcirc c. $3^{2} \times 3^{1} = 27$ \
\bigcirc d. $3^{4} \times 3^{-1} = \frac{1}{27}$

Explanation:

For Question 4:

Step1: Apply exponent addition rule

When multiplying same bases, add exponents: $a^m \times a^n = a^{m+n}$.
$4^2 \times 4^{-6} = 4^{2 + (-6)} = 4^{-4}$

Step2: Rewrite negative exponent

A negative exponent means reciprocal: $a^{-n} = \frac{1}{a^n}$.
$4^{-4} = \frac{1}{4^4}$

Step1: Verify Option A

Apply exponent addition rule: $3^6 \times 3^{-3} = 3^{6-3}=3^3=27$. This is true.

Step2: Verify Option B

Apply exponent addition rule: $3^3 \times 3^{-6} = 3^{3-6}=3^{-3}=\frac{1}{3^3}=\frac{1}{27}$. This is true.

Step3: Verify Option C

Apply exponent addition rule: $3^2 \times 3^1 = 3^{2+1}=3^3=27$. This is true.

Step4: Verify Option D

Apply exponent addition rule: $3^4 \times 3^{-1} = 3^{4-1}=3^3=27
eq \frac{1}{27}$. This is false.

Answer:

C. $\frac{1}{4^4}$

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For Question 8: