Exponents

1. Simplify $(512)^{-2/3}$:

Solution:

$$ (512)^{-2/3} = (2^9)^{-2/3} = 2^{-6} = \frac{1}{64} $$

2. Find the value of x:

(a) Assuming & represents multiplication in $\sqrt{5*5x+2}=2$

Solution:

$$ \sqrt{5*5x+2}=2 \Rightarrow 25x + 2 = 4 \Rightarrow 25x = 2 \Rightarrow x = \frac{2}{25} $$

(b) $5^{x-3}×3^{2x-8}=225$

Solution:

$$ 5^{x-3}×3^{2x-8}=225 \Rightarrow 5^{x-3} = \frac{225}{3^{2x-8}} \Rightarrow 5^{x-3} = \frac{225}{9^{x-4}} \Rightarrow 5^{x-3} = 5^2 \Rightarrow x = 5 $$

3. If $(2^{3x-1}+10)÷7=6$, then find the value of x:

Solution:

$$ (2^{3x-1}+10)÷7=6 \Rightarrow 2^{3x-1} + 10 = 42 \Rightarrow 2^{3x-1} = 32 \Rightarrow 3x - 1 = 5 \Rightarrow x = 2 $$

4. Write in standard form:

(a) $0.0000000777$

Solution:

$$ 0.0000000777 = 7.77 \times 10^{-8} $$

(b) $234.45×10^{12}$

Solution:

$$ 234.45×10^{12} = 2.3445 \times 10^{14} $$

5. Evaluate $[((-2)/3)^{-3}-(-3/4)^{-3} ]÷(3/2)^2$:

Solution:

$$ \frac{(-\frac{2}{3})^{-3}-(-\frac{3}{4})^{-3}}{(\frac{3}{2})^2} = \frac{-\frac{27}{8} + \frac{64}{27}}{2.25} = -\frac{216}{216} = -1 $$