Question

Evaluate (2^-5 x 2^-6)^-4​

Answer 1

Answer:

(2^-5 x 2^-6)^-4= 1.7592186e+13

Answer 2

$\displaystyle \sf{ {( {2}^{ - 5} \times {2}^{ - 6} )}^{ - 4} } = \sf \: {2}^{44}$

Given :

$\displaystyle \sf{ {( {2}^{ - 5} \times {2}^{ - 6} )}^{ - 4} }$

To find :

To simplify the expression

Formula :

We are aware of the formula on indices that :

$\sf{1. \: \: {a}^{m} \times {a}^{n} = {a}^{m + n} }$

$displaystyle \sf{2. \: \: \: { ({a}^{m} )}^{n} = {a}^{mn} }$

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

$\displaystyle \sf{ {( {2}^{ - 5} \times {2}^{ - 6} )}^{ - 4} }$

Step 2 of 2 :

Simplify the given expression

$\displaystyle \sf{ {( {2}^{ - 5} \times {2}^{ - 6} )}^{ - 4} }$

$\displaystyle \sf{ = { \bigg( {2}^{( - 5) + ( - 6)} \bigg)}^{ - 4} }\: \: \: \bigg[ \: \because \:{a}^{m} \times {a}^{n} = {a}^{m + n} \bigg]$

$\displaystyle \sf{ = {( {2}^{ - 11} )}^{ - 4} }$

$\displaystyle \sf{ = {2}^{ \{( - 11) \times ( - 4) \}} }\: \: \: \bigg[ \: \because \:{ ({a}^{m} )}^{n} = {a}^{mn} \bigg]$

$\displaystyle \sf{ = {2}^{44} }$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ find the value of x (2) 5) -³×(2/5) ^18=(2/5)^10x

https://brainly.in/question/47348923

2. If (-2)m+1 × (-2)4 = (-2)6 then value of m =

https://brainly.in/question/25449835

#SPJ3