Question

Simplify the following and write in exponential form. 1/27×3^-3​

Answer 1

$\displaystyle \sf{ \frac{1}{27} \times {3}^{ - 3} } = {3}^{ - 6}$

Given :

The expression

$\displaystyle \sf{ \frac{1}{27} \times {3}^{ - 3} }$

To find :

• Simplify the given expression

• Write in exponential form

Solution :

Step 1 of 3 :

Write down the given expression

The given expression is

$\displaystyle \sf{ \frac{1}{27} \times {3}^{ - 3} }$

Step 2 of 3 :

Simplify the given expression

$\displaystyle \sf{ \frac{1}{27} \times {3}^{ - 3} }$

$\displaystyle \sf{ = \frac{1}{27} \times \frac{1}{{3}^{ 3} } }$

$\displaystyle \sf{ = \frac{1}{ {3}^{3} } \times \frac{1}{{3}^{ 3} } }$

$\displaystyle \sf{ = \frac{1}{ {3}^{3} \times {3}^{3}} }$

$\displaystyle \sf{ = \frac{1}{ {3}^{3 + 3}}}$

$\displaystyle \sf{ = \frac{1}{ {3}^{6}}}$

Step 3 of 3 :

Write in exponential form

$\displaystyle \sf{ \frac{1}{27} \times {3}^{ - 3} }$

$\displaystyle \sf{ = \frac{1}{ {3}^{6}}}$

$\displaystyle \sf{ = {3}^{ - 6}}$

$\boxed{ \: \: \displaystyle \sf{ \frac{1}{27} \times {3}^{ - 3} } = {3}^{ - 6} \: \: }$