Question

simplify each exponential expression using the properties of exponents and match it to the correct answer
i have tried to figure this out and have failed it more times then i care to admit
❤ thanks for your help

Answer 1

3^-3 * 2^-3 *6^3 / (4^0)^2

= 6^-3 * 6^3 / (1)^2

= 1 / 1

= 1

---------------------------------------

2^4 * 3^5 / (2*3)^5

= 2^4 * 3^5 / 2^5 *3^5

= 1/ 2^1

= 1/2

---------------------------

(3 * 2)^4 * 3^-3 / 2^3 * 3

=3^4 * 2^4 * 3^-3 / 2^3 * 3

= 3^1 * 2^4 / 2^3 * 3

= 2^1

= 2

-----------------------

3^2 * 4^3 * 2^-1 / (3 * 4)^2

= 3^2 * 4^3 / 3^2 * 4^2 * 2^1

= 4^1 / 2^1

= 4/2

= 2

Answer 2

Exponential expressions can be represented in form of indices.

The results of the expressions are:

• $\mathbf{ \frac{3^{-3} \cdot 2^{-3} \cdot 6^3}{(4^0)^2} = 1}$.
• $\mathbf{\frac{2^4 \cdot 3^5}{(2\cdot 3)^5} = \frac{1}{2}}$.
• $\mathbf{\frac{(3 \cdot 2)^4 \cdot 3^{-3}}{2^3 \cdot 3} = 2}$.
• $\mathbf{\frac{3^2 \cdot 4^3 \cdot 2^{-1}}{(3\cdot 4)^2} = 2}$

$\mathbf{(a)\ \frac{3^{-3} \cdot 2^{-3} \cdot 6^3}{(4^0)^2}}$

Express 4^0 as 1

$\mathbf{ \frac{3^{-3} \cdot 2^{-3} \cdot 6^3}{(4^0)^2} = \frac{3^{-3} \cdot 2^{-3} \cdot 6^3}{1^2}}$

Express 1^2 as 1

$\mathbf{ \frac{3^{-3} \cdot 2^{-3} \cdot 6^3}{(4^0)^2} = 3^{-3} \cdot 2^{-3} \cdot 6^3}$

Express 6 as 2 * 3

$\mathbf{ \frac{3^{-3} \cdot 2^{-3} \cdot 6^3}{(4^0)^2} = 3^{-3} \cdot 2^{-3} \cdot (2 \times 3)^3}$

Expand

$\mathbf{ \frac{3^{-3} \cdot 2^{-3} \cdot 6^3}{(4^0)^2} = 3^{-3} \cdot 2^{-3} \cdot 2^3 \times 3^3}$

Rewrite as:

$\mathbf{ \frac{3^{-3} \cdot 2^{-3} \cdot 6^3}{(4^0)^2} = 3^{-3} \times 3^3 \cdot 2^{-3} \times 2^3 }$

Apply law of indices

$\mathbf{ \frac{3^{-3} \cdot 2^{-3} \cdot 6^3}{(4^0)^2} = 3^{-3+3} \cdot 2^{-3+3} }$

$\mathbf{ \frac{3^{-3} \cdot 2^{-3} \cdot 6^3}{(4^0)^2} = 3^{0} \cdot 2^0 }$

$\mathbf{ \frac{3^{-3} \cdot 2^{-3} \cdot 6^3}{(4^0)^2} = 1 \cdot 1 }$

$\mathbf{ \frac{3^{-3} \cdot 2^{-3} \cdot 6^3}{(4^0)^2} = 1}$

$\mathbf{(b)\ \frac{2^4 \cdot 3^5}{(2\cdot 3)^5}}$

Open bracket

$\mathbf{\frac{2^4 \cdot 3^5}{(2\cdot 3)^5} = \frac{2^4 \cdot 3^5}{2^5 \cdot 3^5}}$

Apply laws of indices

$\mathbf{\frac{2^4 \cdot 3^5}{(2\cdot 3)^5} = 2^{4-5} \cdot 3^{5-5}}$

$\mathbf{\frac{2^4 \cdot 3^5}{(2\cdot 3)^5} = 2^{-1} \cdot 3^{0}}$

$\mathbf{\frac{2^4 \cdot 3^5}{(2\cdot 3)^5} = 2^{-1} \cdot 1}$

$\mathbf{\frac{2^4 \cdot 3^5}{(2\cdot 3)^5} = 2^{-1}}$

Rewrite as:

$\mathbf{\frac{2^4 \cdot 3^5}{(2\cdot 3)^5} = \frac{1}{2}}$

$\mathbf{(c)\ \frac{(3 \cdot 2)^4 \cdot 3^{-3}}{2^3 \cdot 3}}$

Expand bracket

$\mathbf{\frac{(3 \cdot 2)^4 \cdot 3^{-3}}{2^3 \cdot 3} = \frac{3^4 \cdot 2^4 \cdot 3^{-3}}{2^3 \cdot 3}}$

Apply law of indices

$\mathbf{\frac{(3 \cdot 2)^4 \cdot 3^{-3}}{2^3 \cdot 3} = 3^{4-3-1} \cdot 2^{4-3}}$

$\mathbf{\frac{(3 \cdot 2)^4 \cdot 3^{-3}}{2^3 \cdot 3} = 3^{0} \cdot 2^{1}}$

$\mathbf{\frac{(3 \cdot 2)^4 \cdot 3^{-3}}{2^3 \cdot 3} = 1 \cdot 2}$

$\mathbf{\frac{(3 \cdot 2)^4 \cdot 3^{-3}}{2^3 \cdot 3} = 2}$

$\mathbf{(d)\ \frac{3^2 \cdot 4^3 \cdot 2^{-1}}{(3\cdot 4)^2}}$

Express 4 as 2^2

$\mathbf{\frac{3^2 \cdot 4^3 \cdot 2^{-1}}{(3\cdot 4)^2} = \frac{3^2 \cdot (2^2)^3 \cdot 2^{-1}}{(3\cdot 2^2)^2}}$

$\mathbf{\frac{3^2 \cdot 4^3 \cdot 2^{-1}}{(3\cdot 4)^2} = \frac{3^2 \cdot 2^6 \cdot 2^{-1}}{(3\cdot 2^2)^2}}$

Open bracket

$\mathbf{\frac{3^2 \cdot 4^3 \cdot 2^{-1}}{(3\cdot 4)^2} = \frac{3^2 \cdot 2^6 \cdot 2^{-1}}{3^2\cdot 2^4}}$

Apply law of indices

$\mathbf{\frac{3^2 \cdot 4^3 \cdot 2^{-1}}{(3\cdot 4)^2} = 3^{2-2} \cdot 2^{6-1-4}}$

$\mathbf{\frac{3^2 \cdot 4^3 \cdot 2^{-1}}{(3\cdot 4)^2} = 3^{0} \cdot 2^{1}}$

$\mathbf{\frac{3^2 \cdot 4^3 \cdot 2^{-1}}{(3\cdot 4)^2} = 1 \cdot 2}$

$\mathbf{\frac{3^2 \cdot 4^3 \cdot 2^{-1}}{(3\cdot 4)^2} = 2}$

Read more about indices and exponential expressions at:

https://brainly.com/question/12916986