Question

(-2)m+¹+(-2)⁴=(-2)6=m=​

Answer 1

SOLUTION

TO DETERMINE

The value of m when

$\sf{ {( - 2)}^{m + 1} \times {( - 2)}^{4} = {( - 2)}^{6} }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula on indices that

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

EVALUATION

$\sf{ {( - 2)}^{m + 1} \times {( - 2)}^{4} = {( - 2)}^{6} }$

$\sf{ \implies {( - 2)}^{m + 1 + 4} = {( - 2)}^{6} }$

$\sf{ \implies {( - 2)}^{m + 5} = {( - 2)}^{6} }$

$\sf{ \implies m + 5 = 6}$

$\sf{ \implies m = 6 - 5}$

$\sf{ \implies m = 1}$

FINAL ANSWER

The required value m = 1

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Answer 2

Given : $\sf{(-2)^{m+1} \times(-2)^{4}=(-2)^{6}}$

To Find : Value of m in the Given Expression

$------------------------------$

$\sf{\left(-2\right)^{m+1}\left(-2\right)^4=\left(-2\right)^6}$

• Apply Exponent Rule : $\sf{a^b\times a^c=a^{b+c}}$

$\to\sf{\left(-2\right)^{m+1+4}=\left(-2\right)^6}$

$\to\sf{\left(-2\right)^{m+5}=\left(-2\right)^6}$

• If $\sf{a^{f\left(x\right)}=a^{g\left(x\right)}}$ , then $\sf{f\left(x\right)=g\left(x\right)}$

$\to\sf{m+5=6}$

• Subtract 5 from both Sides

$\to\sf{m+5-5=6-5}$

$\to\sf{m=1}$