Question

Compute:
(-3)^4-(4√3)^0×(-2)^5÷(64)^2/3​

Answer 1

Answer:

83

Step-by-step explanation:

$(-3^{4} )-(3\sqrt{3} )^0*(-2^{5} ) / (64)^{2/3}$

$81 - 1 * \frac{-32}{16}$

16 * -2 is -32 so those get cancelled resulting in ,

$81 -1 *-2$

$81 + 2$

$83$

The Final Answer is 83

Answer 2

$\displaystyle \sf{ {( - 3)}^{4} - {(4 \sqrt{3}) }^{0} \times {( - 2)}^{5} \div {(64)}^{ \frac{2}{3} } } = 83$

Correct question :

$\displaystyle \sf{Compute \: \: {( - 3)}^{4} - {(4 \sqrt{3}) }^{0} \times {( - 2)}^{5} \div {(64)}^{ \frac{2}{3} } }$

Given :

$\displaystyle \sf{ {( - 3)}^{4} - {(4 \sqrt{3}) }^{0} \times {( - 2)}^{5} \div {(64)}^{ \frac{2}{3} } }$

To find :

Simplify the expression

Formula :

We are aware of the formula on indices that :

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

$\displaystyle \sf{2. \: \: \: \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }$

$\displaystyle \sf{3. \: \: \: { ({a}^{m} )}^{n} = {a}^{mn} }$

$\displaystyle \sf{4. \: \: {a}^{0} = 1}$

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

$\displaystyle \sf{ {( - 3)}^{4} - {(4 \sqrt{3}) }^{0} \times {( - 2)}^{5} \div {(64)}^{ \frac{2}{3} } }$

Step 2 of 2 :

Simplify the given expression

$\displaystyle \sf{ {( - 3)}^{4} - {(4 \sqrt{3}) }^{0} \times {( - 2)}^{5} \div {(64)}^{ \frac{2}{3} } }$

$\displaystyle \sf{ = {( - 3)}^{4} -\bigg[{(4 \sqrt{3}) }^{0} \times {( - 2)}^{5} \div {(64)}^{ \frac{2}{3} } \bigg] }$

$\displaystyle \sf{ = {( - 3)}^{4} - \bigg[ 1 \times {( - 2)}^{5} \div {(64)}^{ \frac{2}{3} } \bigg] } \: \: \: \bigg( \: \because \: {a}^{0} = 1 \bigg)$

$\displaystyle \sf{ = {( - 3)}^{4} -\bigg[ {( - 2)}^{5} \div {( {2}^{6} )}^{ \frac{2}{3} } \bigg] }$

$\displaystyle \sf{ = {( 3)}^{4} +\bigg[{( 2)}^{5} \div {( {2}^{} )}^{6 \times \frac{2}{3} }\bigg] }$

$\displaystyle \sf{ = 81 + \bigg[{( 2)}^{5} \div {( {2}^{} )}^{4}\bigg] }$

$\displaystyle \sf{ = 81 + \bigg[{( 2)}^{5 - 4}\bigg] }$

$\displaystyle \sf{ = 81 + \bigg[{( 2)}^{1}\bigg] }$

$\displaystyle \sf{ = 81 + 2 }$

$\displaystyle \sf{ = 83}$

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