Question

3^-5x10^-5x125/5^-7x6^-5, simplify and express with positive power

Answer 1

Answer:

Step-by-step explanation:

Answer 2

$\bf \red{\frac{ {3}^{ - 5} \times {10}^{ - 5} \times 125 }{ {5}^{ - 7} \times {6}^{ - 5} } = {5}^{5}}$

Given:

• $\frac{ {3}^{ - 5} \times {10}^{ - 5} \times 125 }{ {5}^{ - 7} \times {6}^{ - 5} }$

To find:

• Simplify and express with positive powers.

Solution:

Formula to be used:

1. ${a}^{n} \times {a}^{m} = {a}^{n + m}$
2. $\frac { {a}^{n} }{ {a}^{m} } = {a}^{n - m}$
3. $\frac{1}{ {a}^{ - n} } = {a}^{n}$
4. ${(ab)}^{n} = {a}^{n} \times {b}^{n}$

Step 1:

$= \frac{ {3}^{ - 5} \times {(5 \times 2)}^{ - 5} \times {5}^{3} }{ {5}^{ - 7} \times {(2 \times 3)}^{ - 5} }$

or

Using formula 4 simplify terms, as shown below

$= \frac{ {3}^{ - 5} \times {5^{ - 5} \times 2}^{ - 5} \times {5}^{3} }{ {5}^{ - 7} \times {2^{ - 5} \times 3}^{ - 5} }$

Step 2:

Apply formula 1 and 2 to simplify further.

$= {3}^{ - 5 + 5} \times {5^{ - 5 + 3 + 7} \times 2}^{ - 5 + 5}$

or

$= {3}^{ 0} \times {5^{ 5} \times 2}^{0}$

as;

$\because {a}^{0} = 1$

so,

$=1\times 5^{ 5} \times 1$

or

$= 5^{ 5}$

Thus,

$\bf \frac{ {3}^{ - 5} \times {10}^{ - 5} \times 125 }{ {5}^{ - 7} \times {6}^{ - 5} } = {5}^{5}$

Learn more:

1) simplify 12⁴×9³×4/6³×8²×27

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