Question

find the value of x if
${128}^{x \: } \div {4}^{x} = {16}^{x}$
​

Answer 1

Step-by-step explanation:

$128 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \\ 128 = {2}^{7} \\ 4 = 2 \times 2 = {2}^{2} \\ 16 = 2 \times 2 \times 2 \times 2 \\ 16 = {2}^{4} \\ {128}^{x} \div {4}^{x} = {16}^{x} \\ {( {2}^{7} )}^{x} \div { ({2}^{2} )}^{x} = {16}^{x} \\ {2}^{7x} \div {2}^{2x} = {16}^{x} \\ {2}^{7x} \times \dfrac{1}{ {2}^{2x} } = {16}^{x} \\ {2}^{7x - 2x} = { ({2}^{4}) }^{x} \\ {2}^{5x} = {2}^{4x} \\ \bold{ \blue {comparing \: exponent}} \\ 5x = 4x \\ 5x - 4x = 0 \\ x = 0$

$\bold{ \large{ \underline{ \pink{formula \: used \longrightarrow}}}} \\ 1. \: \: \: \large{ \boxed{\boxed{\bold{\blue{ {a}^{m} {a}^{n} = {a}^{m + n} }}}}} \\ 2. \: \: \: \: \large{ \boxed{ \boxed{\bold{\blue{{({a}^{m})}^{n}={a}^{m + n}}}}}}$

Answer 2

Step-by-step explanation:

Here is your answer dear

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